The duty to indemnify means the duty to pay "all sums" for which the insured is held liable, up to a set policy limit.
To settle reasonable claims
In some jurisdictions, there is a third duty, the duty to settle a reasonably clear claim against the insured. The duty is of greatest import during situations in which the settlement demand equals or exceeds the policy limits.
In that case, the insurer has an incentive not to settle, since if it settles, it will certainly pay the policy limit. But this interest is at odds with the interest of its insured. The company has incentive not to settle since if the case goes to trial, there are only two possibilities: its insured loses and insurer pays the policy limits (nothing gained nothing lost), or its insured wins, leaving the insurer with no liability. But, if the insurer refuses to settle, and the case goes to trial, the insured might be held liable for a sum far exceeding the settlement offer. In turn, the plaintiff might then attempt to recover the difference between the policy limits and the actual judgment by obtaining writs of attachment or execution against the insured's assets.
This is where the duty to settle comes in. To avoid endangering an insured to gain a remote possibility of avoiding paying on the policy, the duty to defend obligates the insurance company to settle reasonably clear claims. The standard judicial test is that an insurer must settle a claim if a reasonable insurer, notwithstanding any policy limits, would have settled the claim.
Effects of breach
An insurer who breaches any of these three duties may be held liable for the tort of insurance bad faith in addition to breach of contract.
Occurrence v. Claims-Made Policies
Traditionally, liability insurance was written on an occurrence basis, meaning that the insurer agreed to defend and indemnify against any loss which allegedly "occurred" as a result of an act or omission of the insured during the policy period. This was originally not a problem because it was thought that insureds' tort liability was predictably limited by doctrines like proximate cause and statutes of limitations.
Claims-made policies enable insurers to again sharply limit their own long-term liability on each policy and in turn, to close their books on policies and record a profit. Hence, they are much more affordable than occurrence policies and are very popular for that reason. Of course, claims-made policies shift the burden to insureds to immediately report new claims to insurers. They also force insureds to become more proactive about risk management and finding ways to control their own long-tail liability.
Claims-made policies often include strict clauses that require insureds to report even potential claims and that combine an entire series of related acts into a single claim. Claims-made coverage also makes it harder for insureds to switch insurers, as well as to wind up and shut down their operations. It is possible to purchase "tail coverage" for such situations, but only at premiums much higher than for conventional claims-made policies, since the insurer is being asked to re-assume the kind of liabilities which claims-made policies were supposed to push to insureds to begin with.