Thanks for the chance to help. I am an attorney with over 12 years experience. Hopefully I can help you with your legal question.
You can still sue...but if the damages exceeds the liability limit on the insurance policy
, you would need to collect the additional money from the driver.
Under the law in Texas, if an individual is negligent, and the negligence results in economic loss, the victim can sue to recover for the losses. If the individual is insured, the insurance is required to pay, up to the insurance policy limit, if negligence is established (either by settlement or via a court case).
If the damages exceed the insurance limit, the individual then becomes personally responsible for the remainder of the damages
So you can sue for the entire loss. Collect the damage limit from the insurance company, and seek the remainder from the individual. If they refuse to agree to pay, you will need to sue them and obtain a judgment to force them to pay.