It all depends on whether the loan was in your name or not. If the loan is exclusively in your wife’s name, the car becomes part of her estate. If you’re the executor of her estate, you can use her savings or other funds she left to you to pay off the loan.
If you don’t have the money from her will, you’ll have to pay off the loan yourself. The smart move here, if you don’t want the car, is to pay enough toward the loan to eradicate the negative equity and then sell the car.
If your name is on the loan, and she was just a cosigner, you’re free to do whatever you want. Because the loan is upside-down, you won’t be able to sell it without a balance left on the loan. You won’t be able to refinance it either. Hope this helps.”