What can you do if you have only liability insurance and your parked car is hit by an unknown driver?

Unles your daughter has collision or UMPD coverage on her policy, there's nothing the insurance carrier can do for you. In a case like this, it really does come down to "you get what you pay for." If a premium wasn't paid to the carrier for the collision or UMPD coverage, they can't help. By not carrying collision or UMPD coverage on the car, it's assumed that your daughter understands she will be paying out-of-pocket for any damage to her car.