Car accident, need some advice?

If you are over 21 and you get in a car accident and your insurance only covers up to 15,000 of bodily injury. can they file a law suit if their damages exceed this? if so who is liable for this? the driver, or the person who's the main policy holder. that is, if the driver is a student and has no money, can his dad, who is the main policy holder, be responsible even though he had nothing to do with the accident?