There are such things as "wasting" policies, meaning that there is a single limit for defense and indemnity. That is not what you see in auto policies. You see wasting policies sometimes in commercial settings.
I think what brcase is referring to is when there is questionable liability on the part of the insured, or questionable damages. In that case, and adjuster may well decide that they will offer cash to resolve the matter quickly (whether or not suit has already been filed) rather than defend it if it can be settled quickly. But, if turned down, then they will defend all the way. But as long as there is coverage, the insurance company will have to keep defending until the claim is resolved, or possibly the limits are exhausted. These days, it seems like 95% or greater of cases get resolved short of a trial.