Blue Sky Letters
Usually the most an insurance company will pay to settle the case is the limit of liability it sold to the insured.
If the insured purchased $50,000 in coverage, the insurance company usually isn’t going to pay more than that to settle a claim. (There is, however, a basically uncapped pool of money available to defend that claim.)
However, there are situations where an insurance company issues a Blue Sky letter to insureds. What’s a Blue Sky letter? Basically a promise that the insurance company will pay the full amount of any judgment even if it exceeds the limits purchased by the insured.
(In some senses it should be called the "sky's the limit" letter.)


When and why would an insurance company do such a thing?
Usually it’s because the insurance company has been given a chance to protect its insured by settling a claim within policy limits but has decided to gamble that it can get it resolved later for less money.
An example: An injured driver offers to release his claim for $45,000. There is a $50,000 policy limit. The insurance company decides that maybe it can settle the claim for $40,000 so it rejects the $45,000 demand. That’s fine, but if the verdict comes back for $95,000, the insurance company should have to cover it, not the insured. The Blue Sky letter advises the insured what’s going on and that the insurance company is gambling with its own money.
During discovery we get to find out how much coverage the defendant carried. Even though Blue Sky letters are not part of the defendant’s policy, they are essentially like an addendum that says the limit is no longer $50,000, the limit is the full amount of the verdict.
That’s why Blue Sky letters are discoverable and must be disclosed during discovery.