What is the potential liability of a person who insures someone else's car?

The short answer here is that you can insure the vehicle of another under certain conditions and generally only if you have the owner’s permission as well as an insurable interest in that vehicle. In order to purchase insurance for something such as property, the person buying the insurance must have some financial interest in it. And generally too insurance insures the car.  But the long answer here is I would not think that the scenario as you have paid it out here is a good one to purchase insurance.  I think that the insurance company will have a lot of ammunition to disclaim coverage - that is what you meant by denying the claim - and yes, that could leave you on the hook.  Good luck.