Will progressive insurance pay for your car damage that was caused while your car was parked legally in your apartment parking lot if the driver of the car did not have insurance but the person who ha?

You didn't complete your question so I will try to answer it as best I can. Any policy no matter what company it is will be the same if you have the same coverage. If the other party had no insurance on the vehicle then your uninsured motorist coverage will pay for your damage just as if they had coverage up to you limit of UM coverage. If the other person was using someone else's car and the car owner had coverage then his insurance will pay for the damages. Liability coverage follows the car generally. If your UM coverage has to pay for the damages, they will go after the car owner and the driver for reimbursement of the loss.