State laws and insurance policy terms vary and we are not familiar with all states liability laws. In general though, if the added driver is your minor child or dependant, then the policyholder will normally be held responsible for that driver's actions in their vehicle.

Other "additional drivers" that the owner and policyholder gives permission to operate the policyholder’s vehicle, the policyholder may be held accountable for their actions behind the wheel as well. This is called vicarious liability.

Vicarious liability is a legal concept, which refers to one party being held liable for the injury or damage sustained by another party, despite the fact that they had no active involvement in the incident. So as the policyholder you may not be driving when an accident occurs but if you are the car's owner and gave the driver permission to drive your car and there is an accident you (as well as the actual driver) may be held responsible.

But, if it just happens to be an additional driver driving someone else’s vehicle, there should not be any extra liability placed upon you. Because, in general, by adding someone as a driver to your policy, you are letting the insurance company know that person will be driving the vehicle(s) on your policy with some kind of frequency.

Due to differing state liability laws as well as varying terms of insurance policies, you will need to check with your insurance company to be sure what your responsibilities are as a policyholder who has additional drivers listed on their policy.