Can a parent be sued for thier 19 year old son's car accident if he injured people?

There is more information needed.  If the parents own the vehicle they can be sued for the actions of their son while he was driving the car.  Any person who allows another to drive their vehicle can be held liable for the actions of the driver.  If the vehicle was stolen they can not be held responsible. IF your son was the owner of the car and it was insured to only him and it was registered to him the parents do not have liabilty for his actions.    Without more information I can not give a more substantial answer.