If you are at fault in an accident then your liability coverages would not cover your vehicle so you could not make a first party claim with them. You would need physical damage coverages of collision and comprehensive to cover damages to your own vehicle if you are at fault in an accident.

If you were in an accident where your car collided with another object, such as a pole or car then you would make a claim against collision coverage and if your car was declared a total loss then your insurance company would work with you on a settlement for the actual cash value (ACV) of the vehicle. If you owned the car, meaning without a lien holder that needed to be paid off, then you would receive a check for the value of the vehicle.

With only liability coverages then your property damage coverages only cover the property of others that you may cause damage to, not your own car. PD covers you if your car damages someone else's property. Usually it is their car, but it could be a fence, a house or any other property damaged in an accident. It also provides you with legal defense if another party files a lawsuit against you.

If instead you were hit by another person then in most states you could make a claim against their property damage liability coverages. With this third party claim the at-fault party's insurance company would send their insurance adjuster to help determine the value of your vehicle and this is who you would work with to get a settlement.