HAMILTON, Circuit Judge.
This appeal illustrates a recurring issue for liability insurers and their insureds: how to determine whether the insurer owes a duty to defend its insured when a claim is first asserted against the insured, before the insurer knows the underlying facts. The insured here was Chicago Abstract Title Agency LLC, which was in the title and escrow services business. In 2008, Chicago Abstract was sued in state court by a title insurance company and two financial firms. Chicago Abstract tendered these lawsuits to its “errors and omissions” liability insurer, plaintiff Title Industry Assurance Company, R.R.G., known in this case as TIAC. TIAC then faced a choice. It could (a) defend Chicago Abstract without reservation; or (b) defend while reserving its rights; or (c) seek a declaratory judgment concerning the scope of coverage. TIAC could also (d) decline to defend, but only if the allegations in the complaints against Chicago Abstract clearly fell outside the scope of the insurance policy, and then only at its peril. Under Illinois law, when a liability insurer unjustifiably refuses to defend a suit against its insured, the insurer will be estopped from later asserting policy defenses to coverage.
TIAC declined to defend the suits. The suits proceeded and years passed without further communications between TIAC and its insured. In 2014, one of the state court plaintiffs, Coastal Funding, LLC, filed a fourth amended complaint against Chicago Abstract. An attorney appointed by TIAC then made a belated appearance in that case. At about the same time, TIAC filed this diversity jurisdiction action in federal court, seeking a declaration that coverage was unavailable primarily because of two exclusions in the policy. Chicago Abstract did not defend in the federal case (the company had been involuntarily dissolved in 2009), but two of the state-court plaintiffs — Coastal Funding and First American Title Insurance Company — appeared in this federal case as defendants. To avoid confusion, we refer to these two firms as the Claimants.
TIAC and the Claimants filed cross-motions for summary judgment. The district court granted judgment to the Claimants. We affirm. We disagree with portions of the district court opinion, particularly its ruling that TIAC was required to plead legal theories in its federal complaint. That ruling is squarely at odds with settled federal pleading practice. See Johnson v. City of Shelby, 574 U.S. -, 135 S.Ct. 346, 190 L.Ed.2d 309 (2014) (summarily reversing dismissal of action for failure to identify legal theory in complaint). Nevertheless, we agree that the undisputed facts show that TIAC breached its duty to defend Chicago Abstract in the underlying litigation. TIAC is therefore estopped from asserting at this very late stage any policy defenses to coverage that might have been available if TIAC had made a different choice when the complaints were first tendered.
I. Undisputed Facts and Procedural Background
A. Errors and Omissions Policy
Chicago Abstract was a title insurance agency operating in Cook County, Illinois. As an agent for First American, a title insurance company with a nationwide footprint, Chicago Abstract provided property owners and lenders with real estate closing, loan closing, and title and escrow services. In 2008, TIAC issued to Chicago Abstract an “Abstracters, Title Insurance Agents and Escrow Agents Professional Liability Insurance” policy, more commonly known as an errors and omissions policy. The policy provided that TIAC would [881]*881pay costs for which its “Insured” became liable “by reason of a wrongful act ... aris[ing] out of professional services rendered or that should have been rendered.” The term “Insured” was defined to include Chicago Abstract as well as its members and employees acting within the scope of their duties. Coverage applied both to acts occurring during the policy period and to prior acts if, as of the policy’s effective date, the Insured had no knowledge of those prior acts.
The policy listed two exclusions relevant in this appeal. Under exclusion (a), coverage did not apply to any claim arising out of or relating to “any dishonest, fraudulent, criminal, malicious or intentional wrongful acts committed by or at the direction of the Insured.” A caveat in the policy, labeled condition (1), stated that whenever exclusion (a) was triggered, insurance would remain available for each Insured “who did not personally commit or personally participate in committing any of the wrongful acts described in [that] exclusion ... and who had neither notice nor knowledge of such wrongful acts, if such Insured, upon receipt of notice or knowledge thereof, immediately notifies the Company of the aforesaid wrongful acts.” Under exclusion (j), coverage did not apply to any claim arising out of or relating to “any defalcation, commingling of, or failure to pay any funds, notes, drafts, or other negotiable instruments.”
B. Underlying Complaints and Procedural History
In the fall of 2008, Chicago Abstract was underwater and failing fast. Records were out of order. Transactions were askew. Employees were unsupervised. Most alarming, an outside audit uncovered a significant shortfall in the agency’s escrow account. In this unfolding crisis, without the benefit of a comprehensive investigation and with only a hazy understanding of the facts, First American and two lenders that had done business with Chicago Abstract sought help in court.
On November 5, 2008, First American sued Chicago Abstract and its two members, Michael Rons and Steve Knupp, in the Circuit Court of Cook County. First American alleged that Chicago Abstract had facilitated escrow closings for “irregular and suspicious” real estate “flip” transactions using First American’s insurance policies and closing protection letters. A “flip” or A-B-C transaction involves an investor (B) who buys discounted property from a defaulting homeowner or foreclosing lender (A) using a short-term unsecured loan and then immediately “flips” the property by selling to a third-party buyer (C) for a higher price. Assuming both sides of the transaction close, the investor (B) pays off the short-term loan and pockets the profits. First American’s complaint accused Chicago Abstract of executing “flip” transactions “contrary to the spirit and purpose” of its agency contract. First American added that Chicago Abstract was not maintaining proper documentation; that Chicago Abstract had commingled escrow funds belonging to property owners, investors, and lenders; and that Chicago Abstract may have misappropriated some of those funds. First American sought emergency injunctive relief, up to and including appointment of a receiver, as well as damages for breach of contract.
Several weeks later, 1st Funding Source, LLC, a private capital firm, intervened in the First American action. 1st Funding had agreed to finance the A-B side of four “flip” transactions for which Chicago Abstract served as title agent. For each transaction, Chicago Abstract was authorized to disburse the short-term loan proceeds only on condition that both sides (A-B and B-C) had irrevocably closed. Chicago Abstract allegedly breach[882]*882ed its agreement with 1st Funding by disbursing the proceeds before ensuring that the B-C transaction closed. 1st Funding pled counts for breach of contract, breach of fiduciary duty, and negligence.
Finally, on Christmas Eve 2008 — less than two months after First American filed suit — Coastal Funding brought a separate action in the Circuit Court of Cook County against Chicago Abstract, First American, and a person named Donnel Thomas (elsewhere spelled “Donell”). Like 1st Funding, Coastal Funding had supplied short-term financing for “flip” transactions for which Chicago Abstract served as title agent. Back in October 2008, Coastal Funding had wired $1,370,000 into Chicago Abstract’s general escrow account with the expectation that the funds would be segregated in a fiduciary trust account. According to Coastal Funding, Chicago Abstract breached its fiduciary duty and committed the tort of conversion by “misappropriating” those funds. Coastal Funding also alleged that Donnel Thomas duped it into participating in a Ponzi scheme using Chicago Abstract’s services and that the “flip” transactions — which it had believed were lawful and legitimate — were mere stages of the scheme.
Chicago Abstract tendered the three underlying complaints to TIAC “for defense and indemnification” on February 3, 2009. On July 8, 2009, Chicago Abstract, operating by then under receivership, notified TIAC of two potential claims by First American for missing escrow funds. In letters dated July 31 and August 13, 2009, TIAC denied coverage for the underlying suits and the potential claims. The denial letters cited policy exclusions (a) and (j) and asserted that the policy did not cover the remedies that the state court plaintiffs sought. TIAC reiterated its coverage position without explanation in a letter dated August 12, 2011.
The state-court litigation proceeded without TIAC’s involvement. In 2011, the state court entered two orders granting default judgment against Chicago Abstract on six counts of Coastal Funding’s then-controlling complaint. In 2013, First American and 1st Funding reached a settlement agreement that had the effect of resolving 1st Funding’s claims against Chicago Abstract. First American has not settled with Chicago Abstract.
In 2014, Coastal Funding filed its fourth amended complaint in state court.1 Chicago Abstract defaulted. Shortly after that, in an about-face, TIAC appointed counsel to defend Chicago Abstract in the Coastal Funding action. The state court then entered an order vacating the default, though the parties dispute whether that order also vacated the prior default judgments. (That’s a question for the state courts; we do not consider it here.)
Around the same time that it began defending in state court, TIAC filed this action for a declaration of non-coverage on the bases of exclusions (a) and (j), as well as a third defense no longer at issue. Claimants First American and Coastal Funding appeared as defendants in the federal action. Coastal Funding filed a counterclaim seeking a declaration that TIAC breached its duty to defend Chicago Abstract. On the parties’ cross-motions for summary judgment, the district court granted judgment in favor of the Claimants, finding TIAC in breach and holding [883]*883that TIAC is estopped from asserting any defenses to coverage. Title Industry Assurance Co. v. Chicago Abstract Title Agency, No. 14 C 1906, 2015 WL 5675544, at *6-7 (N.D. Ill. Sept. 24, 2015). This appeal followed.
II. Analysis
We review de novo the district court’s grant of summary judgment, viewing all facts and drawing all reasonable inferences in favor of TIAC, the party against whom judgment was entered. Ezell v. City of Chicago, 846 F.3d 888, 892 (7th Cir. 2017), citing Dunnet Bay Construction Co. v. Borggren, 799 F.3d 676, 688 (7th Cir. 2015). The interpretation of an insurance policy and the contours of the insurer’s duty to defend are questions of state law. Illinois substantive law controls here.
A. The Duty to Defend
Liability insurers often encounter the problem that TIAC faced in this case. Liability insurance policies require insureds to notify their insurers of claims promptly, often on penalty of forfeiting coverage if they delay. Upon receiving such notice, the insurer then must make a prompt decision: will it defend or will it deny coverage? Often, as in this case, the insurer must make this decision before it has time to investigate all the relevant facts.
“The oft-repeated refrain of Illinois insurance law is that an insurer’s duty to defend is ‘much broader’ than its duty to indemnify.” Landmark American Ins. Co. v. Hilger, 838 F.3d 821, 824 (7th Cir. 2016), quoting Crum & Forster Managers Corp. v. Resolution Trust Corp., 156 Ill.2d 384, 189 Ill.Dec. 756, 620 N.E.2d 1073, 1079 (1993). “A duty to defend will arise when the allegations of the underlying complaint may potentially come within the coverage of the policy.” Westfield Ins. Co. v. West Van Buren, LLC, 406 Ill.Dec. 99, 59 N.E.3d 877, 882 (2016). The insurer may not simply refuse to defend a suit against its insured unless it is clear from the underlying complaint “that the allegations fail to state facts which bring the case within, or potentially within, the policy’s coverage.” Employers Ins. of Wausau v. Ehlco Liquidating Trust, 186 Ill.2d 127, 237 Ill.Dec. 82, 708 N.E.2d 1122, 1136 (1999) (citation omitted).
Illinois law provides two avenues for an insurer that is uncertain of its obligations under the policy. It may “defend the suit under a reservation of rights or seek a declaratory judgment that there is no coverage.” Id. An insurer that fails to take either of these actions does so at its peril. If a court later finds that the insurer breached its duty to defend, the insurer will be estopped from asserting policy defenses to coverage. Edward T. Joyce & Associates, P.C. v. Professionals Direct Ins. Co., 816 F.3d 928, 932 (7th Cir. 2016), citing Ehlco Liquidating Trust, 237 Ill.Dec. 82, 708 N.E.2d at 1135.
In deciding whether an insurer breached its duty, Illinois courts ordinarily apply the “eight-corners” rule: “the court ‘compares the four corners of the underlying complaint with the four corners of the insurance policy to determine whether facts alleged in the underlying complaint fall within or potentially within coverage.’ ” American Alternative Ins. Corp. v. Metro Paramedic Services, Inc., 829 F.3d 509, 513-14 (7th Cir. 2016) (citation omitted); see also Taco Bell Corp. v. Continental Casualty Co., 388 F.3d 1069, 1073 (7th Cir. 2004) (insurer’s duty to defend is “determined by the allegations of the complaint ... rather than by what is actually proved”).
When an insurer brings a timely declaratory judgment action, Illinois courts [884]*884may look beyond the four corners of the underlying complaint and consider extrinsic evidence, such as a separate but related pleading. See Pekin Ins. Co. v. Wilson, 237 Ill.2d 446, 341 Ill.Dec. 497, 930 N.E.2d 1011, 1020 (2010) (“To require the trial court to look solely to the complaint in the underlying action to determine coverage would ... greatly diminish a declaratory action’s purpose of settling and fixing the rights of the parties.”) (emphasis and citation omitted). But where the insurer fails to bring a timely declaratory judgment action and the question before the court is whether the insurer breached its duty to defend, the court confines its review to the insurance policy and the underlying complaint, absent unusual circumstances. Compare Hilger, 838 F.3d at 824 (“[W]hen an insurer tries to deny coverage without seeking a declaratory judgment or defending under a reservation of rights ... the relevant question is whether the insurer justifiably refused to defend the action based solely on the allegations in the complaint, so the court’s inquiry is necessarily limited to those allegations.”), with Bartkowiak v. Underwriters at Lloyd’s, London, 395 Ill.Dec. 709, 39 N.E.3d 176, 179, 182 (2015) (trial court did not err in taking account of tortfeasor’s primary insurance coverage that was not specifically referenced in underlying complaint or in defendant’s policy but that was known to defendant at the time it denied coverage, was the basis for that denial, and was an objective, undisputed fact).
In conducting its review, the court liberally construes the underlying complaint and the insurance policy in the manner reasonably most favorable to the insured. The court gives little weight to the legal labels attached to the underlying allegations. Selective Ins. Co. of South Carolina v. Target Corp., 845 F.3d 263, 270 (7th Cir. 2016). Because the duty to defend usually depends on the contents of these written documents — the insurance policy and the complaints against the insured — the issue can often be decided on a motion for summary judgment. E.g., Metro Paramedic, 829 F.3d at 516 (affirming summary judgment for insured); Hartford Casualty Ins. Co. v. Karlin, Fleisher & Falkenberg, LLC, 822 F.3d 358, 361 (7th Cir. 2016) (affirming summary judgment for insurer).
The rule of Illinois law most important here is that if the underlying complaint alleges several theories of recovery, the insurer’s duty to defend arises “even if only one such theory is within the potential coverage of the policy.” Santa’s Best Craft, LLC v. St. Paul Fire & Marine Ins. Co., 611 F.3d 339, 346 (7th Cir. 2010) (citation omitted); see also Nat’l American Ins. Co. v. Artisan & Truckers Casualty Co., 796 F.3d 717, 723 (7th Cir. 2015) (insurer must defend against covered claims despite presence of “proscribed theory of recovery”); Wilson, 341 Ill.Dec. 497, 930 N.E.2d at 1015 n.2 (where insurer has duty to defend against at least one count of underlying lawsuit, it must then defend against all counts).
B. Prior Knowledge Provision
Before digging into the exclusions that TIAC relied upon in its denial letters, we must address an argument that TIAC raised for the first time in federal court— that the prior knowledge provision in the policy’s insuring agreement and in a related question on the insurance application barred coverage of the underlying claims. The prior knowledge provision stated that TIAC would cover damages relating to wrongful acts occurring “prior to the policy period provided that on the effective date of th[e] policy the Insured has no knowledge of such wrongful act[s].”
[885]*885The Claimants argue that TIAC waived its right to rely on the prior knowledge provision by failing to cite that provision in its letters denying coverage. Those letters said nothing about Chicago Abstract’s prior knowledge. In fact, it was not clear that TIAC intended to rely on the prior knowledge provision until it filed its motion for summary judgment in this untimely declaratory judgment action (though TIAC did allude to the provision in its answer to Coastal Funding’s counterclaim). Federal notice pleading requires only a “short and plain statement of the claim showing that the pleader is entitled to relief,” Fed. R. Civ. P. 8(a)(2), so TIAC’s failure to refer to the prior knowledge provision in its declaratory judgment complaint is not fatal. However, Illinois substantive law controls in this diversity dispute. Illinois courts recognize that a “long delay in asserting a policy defense ... may constitute a waiver of that defense,” though the party asserting waiver must prove that it has been prejudiced by the delay. E.g., Rosalind Franklin Univ. of Medicine & Science v. Lexington Ins. Co., 380 Ill.Dec. 89, 8 N.E.3d 20, 44 (2014). Illinois courts also recognize the “mend-the-hold” doctrine, which “preclude[s] insurers from denying a claim on one basis and then changing [the] basis for denial during litigation” if there is evidence of unfair surprise or arbitrariness. E.g., FHP Tectonics Corp. v. American Home Assurance Co., 404 Ill.Dec. 816, 57 N.E.3d 575, 587 (2016); Grinnell Mutual Reinsurance Co. v. LaForge, 369 Ill.App.3d 688, 309 Ill.Dec. 235, 863 N.E.2d 1132, 1140 (2006).
The Claimants rely on the doctrines of both waiver and “mend-the-hold,” arguing that TIAC’s late assertion of the prior knowledge provision prejudiced them because they “did not engage in any discovery related to ‘prior knowledge’ or alleged misrepresentations in the renewal application.” While the Claimants have not made an especially strong showing of prejudice, TIAC has offered no justification for its delay. “[SJtrong proof is not required to show a waiver of a policy defense, but only such facts as would make it unjust, inequitable or unconscionable to allow the defense to be interposed.” Rosalind Franklin Univ., 380 Ill.Dec. 89, 8 N.E.3d at 44 (citation omitted).
Moreover, even if TIAC’s late assertion of the prior knowledge provision could be excused, the assertion would fail on its merits. Chicago Abstract’s errors and omissions policy became effective July 24, 2008. Nothing in the complaints tendered to TIAC implicated Chicago Abstract or its principals (the defendants in the underlying suits) in any misconduct occurring before that date.
To support its denial decision, TIAC points to a letter that Chicago Abstract received from First American and forwarded to TIAC before it denied coverage. In that letter, First American warned that Chicago Abstract might “have liability for numerous matters stemming from the activities within [its] operation,” involving transactions “during a period of time from approximately May 2008-October 2008.” First American’s early guesstimate as to the date range during which problem transactions may have occurred is not a useful measure for determining the point at which Chicago Abstract and its agents were on notice of any wrongful acts. At most, First American’s letter might have prompted TIAC to investigate whether its Insured had advance knowledge of a potential claim. The letter could not justify TIAC’s flat refusal to defend its Insured.
In rejecting TIAC’s reliance on the prior knowledge provision, we do not decide whether the outcome might be different if the summary judgment record contained concrete evidence to .support a finding [886]*886that, as of the policy’s effective date, Chicago Abstract and its principals were on notice of a claim or of conduct likely to result in a claim. The record contains no such concrete evidence. Coastal Funding’s fourth amended complaint — the pleading that precipitated TIAC’s late entry in the underlying litigation — includes a few vague allegations suggesting that Chicago Abstract’s principals may have suspected trouble was afoot during the summer of 2008. But that pleading does not allege— and there is certainly no evidence in the summary judgment record to support a finding — that the principals knew about a Ponzi scheme or any missing funds at that time.
Mere suspicion of questionable transactions does not trigger the prior knowledge provision. That provision requires, well, knowledge. There is no evidence that Chicago Abstract and its principals had such knowledge as of July 24, 2008.2 We therefore do not decide whether, if after-acquired evidence showed that Chicago Abstract or its principals actually knew about wrongful acts and/or looming claims when they applied for coverage, the ordinary estoppel rules would give way. TIAC points to no authority that would require that result, though the equities and policy arguments might support that conclusion. That is not this ease, so we decline to predict how the Illinois Supreme Court would decide that issue. With neither contemporaneous nor after-acquired evidence that would trigger the prior knowledge provision, TIAC’s argument fails on its merits.
C. TIAC’s Bases for Denying Coverage 1. Exclusion (a)
We turn now to the provisions TIAC invoked in denying coverage back in 2009. Exclusion (a) withheld coverage for any claim relating to “any dishonest, fraudulent, criminal, malicious or intentional wrongful acts committed by or at the direction of the Insured.” Exclusion (a) does not justify TIAC’s refusal to defend against the tendered suits.
Later-filed pleadings and subsequent developments show that the Claimants’ damages were attributable at least partly to fraud by someone. But the complaints as tendered did not compel that conclusion. At most they placed TIAC on notice that one or more of the underlying claims might be subject to exclusion (a). The presence of a theory excluded from coverage simply does not excuse an insurer from its duty to defend its insured. Artisan & Truckers, 796 F.Bd at 723; see also Santa’s Best, 611 F.3d at 346 (where underlying complaint presents several theories of recovery, “the duty to defend arises even if only one such theory is within the [887]*887potential coverage of the policy”) (citation omitted).
Most of the allegations in the tendered complaints had no obvious relationship to a fraud claim, though just one path toward a covered claim would have been enough to trigger the duty to defend. First American’s complaint accused Chicago Abstract of breach of contract, and it alleged a host of errors and omissions that could arise as easily from negligence as from intentional wrongdoing. The complaint also alleged “irregular and suspicious” real estate transactions and suggested that Chicago Abstract’s agents may have misappropriated escrow funds. Those nebulous allegations did not indisputably remove the complaint from coverage, which is what would have been required to avoid the duty to defend. 1st Funding settled and has not appeared in TIAC’s federal case, but nothing in 1st Funding’s complaint changes our analysis. 1st Funding alleged that Chicago Abstract disbursed loan proceeds before all conditions were met. It accused Chicago Abstract of negligence and breaches of contract and fiduciary duty. It did not accuse Chicago Abstract of fraud.
The Coastal Funding complaint presents a somewhat closer question, but the result is the same. Coastal Funding accused Chicago Abstract of misappropriating and/or converting $1,370,000. Conversion is an intentional tort, but conversion does not include as an element the intent to defraud. It does not require proof of a criminal or otherwise culpable mental state. Rather, the tortfea-sor must simply act intentionally in a manner that exercises dominion over the property of another without authorization. Whether he does so maliciously or by innocent mistake, the action is still conversion. See Longo Realty v. Menard, Inc., 405 Ill.Dec. 708, 59 N.E.3d 1, 11 (2016) (“Conversion requires the plaintiff establish by a preponderance of the evidence: (1) the defendant’s unauthorized and wrongful assumption of control, dominion, or ownership over the plaintiffs personal property; (2) the plaintiffs right in the property; (3) the plaintiffs right to immediate possession of the property, absolutely and unconditionally; and (4) the plaintiffs demand for possession of the property.”); Martel Enterprises v. City of Chicago, 223 Ill.App.3d 1028, 164 Ill.Dec. 945, 584 N.E.2d 157, 159 (1991) (“Although conversion is considered an intentional tort because it requires ‘an intentional exercise of dominion or control over a chattel,’ it does not require proof of malice, culpability, or conscious wrongdoing.”) (citations omitted).
Coastal Funding’s allegations of misappropriation and conversion were factually threadbare, amounting to little more than legal conclusions. That’s not surprising, given the urgency with which the complaint had to be prepared. Legal conclusions standing alone will not justify an insurer’s refusal to defend its insured. See Cincinnati Ins. Co. v. Eastern Atlantic Ins. Co., 260 F.3d 742, 745 (7th Cir. 2001) (“What is important is not the legal label that the plaintiff attaches to the defendant’s ... conduct, but whether that conduct as alleged in the complaint is at least arguably within one or more of the categories of wrongdoing that the policy covers.”); International Ins. Co. v. Rollprint Packaging Products, Inc., 312 Ill.App.3d 998, 245 Ill.Dec. 598, 728 N.E.2d 680, 688 (2000) (“The question of coverage should not hinge on the ... whims of the plaintiff in the underlying action.”).3
[888]*888Coastal Funding did plead one fraud count that was more factually robust, but that count named only Donnel Thomas, a third party whose association with Chicago Abstract was unexplained. TIAC could not reasonably have construed the allegations against Thomas as somehow excluding coverage for its Insured. This is particularly so in light of the policy’s condition (1), which provided that the fraud exclusion would not bar coverage for any Insured who neither participated in nor knew about the fraud, provided the Insured notified TIAC upon learning of the misconduct.
The decisive point is that the underlying complaints, whether read individually or together, did not compel the conclusion that the Claimants’ losses were attributable to intentional wrongdoing by Chicago Abstract and its agents. See U.S. Fidelity & Guaranty Co. v. Wilkin Insulation Co., 193 Ill.App.3d 1087, 140 Ill.Dec. 907, 550 N.E.2d 1032, 1036 (1989) (“[Since the underlying claims arise from the same set of circumstances, the allegations in any single complaint can be inferred in the other complaints.”), aff'd, 144 Ill.2d 64, 161 Ill.Dec. 280, 578 N.E.2d 926 (1991). The undisputed facts show that exclusion (a) could not justify TIAC’s refusal to defend its Insured at the time of tender.4
2. Exclusion (j)
TIAC also denied coverage based on exclusion (j), which withheld coverage from any claim relating to “any defalcation, commingling of, or failure to pay any funds.” Exclusion (j) also does not justify TIAC’s denial of coverage.
Defalcation is an undefined term in the policy. The term is commonly used in the bankruptcy context, where it describes a “culpable state of mind” involving “knowledge of, or gross recklessness in respect to, the improper nature of ... relevant fiduciary behavior.” Bullock v. BankChampaign, N.A., 569 U.S. -, -, 133 S.Ct. 1754, 1757, 185 L.Ed.2d 922 (2013). More generally, the term connotes fraud or embezzlement, though broader usages also have been recognized. See Defalcation, Black’s Law Dictionary 506 (10th ed. 2014). As discussed above, TIAC could not refuse to defend its Insured on the basis of a fraud exclusion.
As for commingling, only one underlying pleading — the First American complaint— included such an allegation, and commingling was not an essential aspect of First American’s lawsuit. As for the undefined phrase “failure to pay,” the Claimants argue that they alleged the very opposite in state court: they alleged that Chicago Abstract did pay (i.e., disburse) escrow funds under circumstances in which it should not have done so. TIAC perhaps could have countered that “failure to pay” should be read broadly to encompass Chicago Abstract’s failure to return funds to the lenders, but neither exclusion (j) nor the state court complaints were clear enough to es[889]*889tablish that no claim could possibly fall within the scope of coverage. TIAC might have been able to assert a successful defense to coverage during litigation, but even if that were true, it would not follow that TIAC was entitled to abandon its Insured at the outset of litigation.5
3. Northbrook Property and “Wholly Independent ” Acts
TIAC argues that the district court should have enforced exclusion (a) and/or exclusion (j) on the ground that the underlying complaints included some allegations that, if proved, might have fallen outside the scope of coverage. According to TIAC, “where a claim alleges injuries caused by both excluded acts and non-excluded acts,” the insurer must defend only if the non-excluded acts were “wholly independent” of the excluded acts. TIAC’s proposition is difficult to square with the settled principle of Illinois law that if the “underlying complaints allege several theories of recovery ... the duty to defend arises even if only one such theory is within the potential coverage of the policy.” Santa’s Best, 611 F.3d at 346 (citation omitted). In fact, the cases TIAC cites for its “wholly independent” argument are readily distinguishable from this case and illustrate the narrow application of that rule.
TIAC relies principally on Northbrook Property & Casualty Co. v. Transportation Joint Agreement, 194 Ill.2d 96, 251 Ill.Dec. 659, 741 N.E.2d 253 (2000), where a general liability policy excluded injuries stemming from “ownership, maintenance, use or entrustment” of a vehicle. Id., 251 Ill.Dec. 659, 741 N.E.2d at 254. The underlying complaints alleged that students were injured when a train collided with the insured school district’s school bus. Those complaints “utterly fail[ed] to state facts which either actually or potentially” brought the complaints “within the policy’s coverage.” Id. While the claimants attempted to argue around the vehicle exclusion by characterizing the students’ injuries as resulting from the school district’s failure to select safe bus routes, those allegations were “nothing more than re-phrasings of the fact that the students’ injuries arose from the school districts’ use or operation of a motor vehicle.” Id. The students were harmed in an excluded bus accident. Causation was not in dispute, and state of mind was irrelevant. No set of facts consistent with the allegations in the underlying complaints could have brought those complaints within the scope of coverage.6
[890]*890In this case, when the Claimants filed their initial pleadings, the circumstances surrounding their injuries or possible injuries were murky at best. Records were missing. Transactions were unaccounted for. Chicago Abstract’s escrow account was short of cash, but it was not clear who or what was responsible for the shortage. The Claimants sought emergency judicial intervention to preserve the status quo and to avoid further losses while they sorted through the facts. Their vague pleadings reflected their uncertainty. Many of the allegations related to one another only generally, and at least one theory — in fact, most theories — fell outside exclusions (a) and (j).
First American alleged that Chicago Abstract had engaged in “irregular and suspicious” transactions and that its agents appeared to have commingled and misappropriated escrow funds. But First American also accused Chicago Abstract of failing to account for the funds, failing to turn over records, issuing unauthorized insurance policies, neglecting to supervise its employees, and wrongfully holding itself out as an agent of First American. 1st Funding intervened in the First American action, citing a series of incidents in which Chicago Abstract allegedly disbursed loan proceeds before all conditions were satisfied. Coastal Funding filed a separate complaint in which it speculated that Chicago Abstract may have converted its funds. But in that same complaint, Coastal Funding alleged that it had fallen prey to a Ponzi scheme orchestrated by Donnel Thomas, a third party whose association with Chicago Abstract was unclear.
We now know that Thomas had an inside man at Chicago Abstract: Juan Or-ozco, the employee who was eventually convicted of wire fraud for his part in Thomas’s Ponzi scheme. But the Claimants did not know that or allege that when they filed their complaints in 2008. Nor is there any indication that anyone at TIAC was aware of Orozco’s crimes when it denied coverage in 2009. Even if TIAC had known about Orozco, a fraud claim — unlike a motor vehicle tort, see Northbrook Property, 251 Ill.Dec. 659, 741 N.E.2d at 254 — requires the finder of fact to ascertain the tortfeasor’s state of mind. Before undertaking fact discovery, TIAC could not possibly have known whether its Insured, defined to include not only Chicago Abstract but also its members and employees acting within the scope of their employment, were in on the scheme, aware of the scheme, or innocent victims of the scheme. TIAC could not preemptively refuse to defend its Insured on the basis of facts it did not and could not then know.
The search for Northbrook Property's “wholly independent” cause of injury is futile when the primary cause of injury is unknown. Based on the “eight corners” of the tendered complaints and the insurance policy, see Metro Paramedic, 829 F.3d at 513-14, the undisputed facts show no sufficient basis for TIAC to deny coverage.
D. The Consequences of TIAC’s Breach
When TIAC breached its duty by denying a defense in 2009, it left its Insured high and dry. TIAC complains that Chicago Abstract did not “contest or object to TIAC’s coverage declination.” At oral argument, TIAC took the point one [891]*891step farther, suggesting that because Chicago Abstract did not challenge its denial decision, TIAC was unaware “that there was any suggestion that there might be coverage under the policy.” Nonsense. Chicago Abstract placed TIAC on notice of its claim for coverage when it tendered the underlying complaints. TIAC cites no authority for the proposition that an insured must lodge an exception to a denial decision or follow up, begging for reconsideration. On the contrary, Illinois courts even excuse insureds from complying with otherwise non-negotiable policy duties after receiving denial letters. E.g., Owners Ins. Co. v. Seamless Gutter Corp., 356 Ill.Dec. 137, 960 N.E.2d 1260, 1271 (2011) (“[A]n insurer should not be allowed to assert a blanket denial of coverage and then assert the insured’s failure to provide proof of loss, since the law does not require the insured to perform what appeared to be a useless act.”); Jones v. Universal Casualty Co., 257 Ill.App.3d 842, 196 Ill.Dec. 397, 630 N.E.2d 94, 101 (1994) (same).
When an insurer learns of a claim against its insured, the ball is in the insurer’s court. It may defend under a reservation of rights, or it may seek judicial input as to its obligations under the policy. But if it refuses to defend, it cannot then blame the insured for failing to win it over, particularly where — as here — the insured faces significant exposure and must make prompt and difficult decisions regarding litigation or settlement. Cf. Waste Management, Inc. v. Int’l Surplus Lines Ins. Co., 144 Ill.2d 178, 161 Ill.Dec. 774, 579 N.E.2d 322, 334 (1991) (estoppel did not apply where insurers did not abandon insureds but instead (1) sent letters expressing concerns about coverage, (2) evaluated claims under express reservation of rights, and (3) subsequently sought declaratory judgment).
Though TIAC did appear in the Coastal Funding action and file for declaratory relief in federal court five years later, those long-overdue actions cannot excuse its breach of duty back in 2009. By the time TIAC saw fit to intervene, 1st Funding had settled its claims against Chicago Abstract, which had also defaulted on multiple counts in the Coastal Funding case. “Where an insurer waits to bring its declaratory judgment action until after the underlying action has been resolved by a judgment or a settlement, the insurer’s declaratory judgment action is untimely as a matter of law.” Ehlco Liquidating Trust, 237 Ill.Dec. 82, 708 N.E.2d at 1138; cf. Korte Construction Co. v. American States Ins., 322 Ill.App.3d 451, 255 IlLDec. 847, 750 N.E.2d 764, 770 (2001) (“[T]he insurer must take some action to adjudicate the issue of coverage or undertake to defend the insured under a reservation of rights, and it must take that action within a reasonable time of a demand by the insured.”) (emphasis added).
“The world is a dangerous and litigious place. People and businesses buy liability insurance in large part for peace of mind— the knowledge that if one is sued, the insurer will provide a legal defense.... ” CE Design Ltd. v. King Supply Co., 791 F.3d 722, 727 (7th Cir. 2015) (Hamilton, J., concurring). When an insurer breaches its duty to defend, “it’s not just any breach of contract. An insurer’s breach abandons its insured and deprives it of the peace of mind it has bought.” Id.; see also Pompa v. American Family Mutual Ins. Co., 520 F.3d 1139, 1146 (10th Cir. 2008) (“‘By purchasing insurance, the insured reasonably expects that he will not be required to furnish the cost of defending actions that facially fall within the terms of his policy.’ The insured will be deprived of the peace of mind that insurance promises if the insurer can refuse to defend the case, await developments, and then decide to [892]*892reimburse the insured for defense costs only once it is clear that there was coverage.”) (citations omitted); Cates Construction, Inc. v. Talbot Partners, 21 Cal.4th 28, 86 Cal.Rptr.2d 855, 980 P.2d 407, 416 (1999) (“In general, insurance policies are not purchased for profit or advantage; rather, they are obtained for peace of mind .and security in the event of an accident or other catastrophe.”).
Under Illinois law, an insurer that breaches its duty to defend and abandons its insured is estopped from later invoking policy defenses to indemnity. See Panfil v. Nautilus Ins. Co., 799 F.3d 716, 719 (7th Cir. 2015); Philadelphia Indemnity Ins. Co. v. Chicago Title Ins. Co., 771 F.3d 391, 400 n.6 (7th Cir. 2014). This Illinois rule of estoppel is strong stuff, but it is intended to protect insureds’ reasonable expectations of coverage when they most need it. Because TIAC breached its duty to its Insured, it is barred from asserting any policy defenses to coverage that might have applied otherwise. As a practical matter, this means TIAC is on the hook for the judgment or any reasonable settlement amount that the Claimants ultimately recover against TIAC’s Insured. See Delatorre v. Safeway Ins. Co., 370 Ill.Dec. 880, 989 N.E.2d 268, 276 (2013) (“When an insurer wrongfully refuses to defend [its insured], it is liable ... for breach of contract. The measure of damages for such a contractual breach is generally the amount of the judgment against the insured.”), citing Fidelity & Casualty Co. of New York v. Mobay Chemical Corp., 252 Ill.App.3d 992, 192 Ill.Dec. 191, 625 N.E.2d 151, 155 (1992); see also Guillen v. Potomac Ins. Co. of Illinois, 323 Ill.App.3d 121, 256 Ill.Dec. 51, 751 N.E.2d 104, 114 (2001) (“The measure of damages for ... a breach is generally the amount of the judgment against the insured or of a reasonable settlement, plus any expenses incurred.”), aff'd as modified, 203 Ill.2d 141, 271 Ill.Dec. 350, 785 N.E.2d 1 (2003). In the end, TIAC’s hasty abandonment of its Insured may cost it far more than it would have spent if it had simply honored its duty to defend. The judgment of the district court is
AFFIRMED.