Can parents be sued for liability for a 19-year-old child on their insurance in the event they are charged with causing a personal injury accident?

Generally parent's cannot be held responsible for damages caused a child who has reached the age of majority, which in most states is 18. Four states have different age of majority statutes, they are Alabama and Nebraska 19 years old, Mississippi and Pennsylvania 21 years old (with some annotated exceptions). Regardless of the age responsibility for personal injury claims often depends upon specific circumstances. For example how the injury resulted, was it the result to a traffic accident, on property owned by the parents, can any negligence by other parties be attributed to the injury/damages, and so forth. Personal injury attorneys are very good at "working the system" to obtain the maximum damages award possible. It would be in the best interest of the parties involved to consult an attorney who is versant on state laws pertaining to personal injury claims.