Liability insurance is designed to offer specific protection against third-party insurance claims, i.e., payment is not typically made to the insured, but rather to someone suffering loss who is not a party to the insurance contract. In general, damage caused intentionally as well as contractual liability are not covered under liability insurance policies. When a claim is made, the insurance carrier has the duty (and right) to defend the insured. The legal costs of a defense normally do not affect policy limits unless the policy expressly states otherwise; this default rule is useful because defense costs tend to soar when cases go to trial. In many cases, the defense portion of the policy is actually more valuable than the insurance, as in complicated cases, the cost of defending the case might be more than the amount being claimed, especially in so-called “nuisance” cases where the insured must be defended even though no liability is ever brought to trial.

SOURCE: https://en.wikipedia.org/wiki/Liability_insurance