An insurance policy is a contract. A liability policy requires the insurance company to defend the policyholder against claims that are covered by the policy. But, the insurance company is not going to pay for a claim that it does not know about.
Liability insurance is not an exact science. There are a lot of insurance disputes based on differing interpretations of policy language. Usually the insurance company leans toward positions where there will not be coverage, while the policyholder leans towards there being coverage. But, sometimes the inverse is true. Sometimes a policyholder might be sure that the claim is not covered, but the insurance company takes a more cautious approach. Even if the insurer defends under a reservation of rights, at least the policyholder will have saved the costs of paying the defense lawyer. In other words, not tendering (Lesson 94) a lawsuit to an insurer because of an assumption that there will not be coverage can be a costly decision.
Recall also that policies have notice requirements. (Lessons 90-93). If the liability carrier does not find out about the claim until after the suit is over, it is highly unlikely that the insurer will pay anything. So, if there is a claim that might be covered, the safe bet is to turn it over to the insurer even if you think there won’t be coverage. Who knows, the insurer might come to opposite conclusion.
**NOTE – the calculus is a bit more complicated in “estoppel” jurisdictions like Illinois.**