Public or personal liability (bodily injury) and property damage liability (PL/PD) coverage is typically only the state mandated liability coverages and does not include physical damage coverage. Liability policies usually only cover others that you cause injury to or covers you if your car damages someone else's property.

Comprehensive physical damage coverage is what covers a car if it is stolen so without this type of coverage on your vehicle it is unlikely that your insurance company will cover the vehicle in any way for being stolen from you.

With comprehensive coverage your vehicle would be covered for damages done, if the car is recovered and needs repairs, or deemed a total loss if the car is not found. If the vehicle is determined to be the latter, then your insurance company would settle for the actual cash value of the vehicle.