Well for starters, are you SURE it is your car and not one that looks like yours?
Also, is it a reputable dealer or a buy here, pay here place?
Are you making payments to a bank? The dealership? where to?
Lastly, whoever you are making payments to holds the title. Therefore, the car would have to be retitled in order to be sold. So proof you own the car would not be hard to obtain, just call your bank.
If the dealer you are getting your car fixed at is the place that holds your title, you may have a small problem, but that gives them no right to sell your car. You are making payments and therefore own the car. The repairs are separate from the mechanical work. They can hold your car, for payment, but can not sell it.