It will depend upon variables such as your state's laws and the terms of your policy if this accident would be covered by your insurance or not.

In general an insurance company will extend your coverage to others that drive your car IF you have given the driver permission to operate the vehicle. The permission of the owner to use the vehicle is usually one of the prerequisites for an insurance company to pay a claim.

If this person however was on your insurance policy and normally had access to use the car then the insurance company may not feel as if you needed to be asked every time the car was operated by the other party, blanket permission of use may be seen to have been given. In that case your insurer would usually cover any claims from an accident the person was in.

If a person did not just have unauthorized use of your car but stole your vehicle then you should make a police report and you insurance company would not accept claims for damages the thief caused however if you had comprehensive on your vehicle it should cover the damages to your own vehicle.

To find out if your collision coverage would cover the damages to your vehicle caused by the person that used your vehicle without permission read through the terms of your car insurance policy and speak with your agent. Your agent will know your policy and state laws to determine if claims for this person's accident will be accident will be accepted, meaning both a collision claim for your damages and any liability claims for other damages the person may have caused harm to.

If your insurance company will not cover the accident then you, and anyone else damaged by the driver, may need to take him or her to court and seek a judgment for the damages sustained.