The parents would be liabile under two theories
(1) negligent entrustment: give the car to the teenager knowing he's a bad driver and no insurance. If the teen stole the key, parents might be off hook.
(2) vicarious liability: teenager was running errands for the parents, effectively being parent's agent (or employee). This including driving younger siblings, pick up grocery, or other things usually done by the parents.
As you can see, there are some limited circumstances depending on the detailed facts.
