What if it can be proved that the insurance company was wrong in denying coverage of a claim when a third party is suing the insured?
A June 2017, Texas Supreme Court opinion addresses this issue in the case styled, Great American Insurance Co. v. Hamel. The issue in this case was, what constitutes a full adversarial trial.
In Texas, when someone is being sued and the person being sued cannot get their insurance company to provide a defense and pay the claim, and the person being sued believes his insurance company should be providing a defense and paying the claim, then when a judgment is taken against him, he can assign the claim he has against his insurance company to the person who sued him and obtained a judgment.