Legal Question in Personal Injury in Florida

You can sue, but the question is can you collect more than the policy limits from either the other driver's insurer or his/her personal assets or from another entity affiliated in some way with that driver, such as an employer, family member or partner. Thus analysis requires all the facts, which you may not know, such as whether there is any additional insurance, whether the driver was acting on an errand or in the course of some employment and whether the insurer could abs should have offered their policy limits sooner. This would really require analysis by a skilled attorney.

No. If that were the rule then everyone would just carry the minimum amount of insurance required by law. There is no reason to let people unilaterally limit their own liability for injuries they may inflict in the future.