Without seeing the sales agreement and/or loan agreement, it's impossible to answer your question with any certainty. But assuming that both agreements are fairly standard, boilerplate sorts of things, then here's the basic situation: If your husband, as co-signer, was smart enough to insist on finance insurance on the deal (or if the dealership F&I person was smart enough to sell it with the deal and if neither your grandmother nor your husband opted out of it), then the finance insurance policy will pay-off the car in full just as soon as your husband files a claim and sends the finance insurance company a copy of the death certificate.
If, on the other hand, no finance insurance policy was purchased by your grandmother and your husband at the time of contract signing, then your husband must continue making payments (or must sell the car and use the proceeds to pay-off the loan... whichever he prefers). That's what co-signers do: When the principle borrower cannot pay for any reason -- including death -- then the co-signer must honor the contract.
If finance insurance pays off the car loan, then the car is free and clear, but it's in her name. Therefore, her estate has possession of the vehicle and neither you nor your husband can simply take it -- especially if she's intestate (had no will).
If there is no finance insurance, and your husband, therefore, must pay it off, then even though it's in possession of her estate it's a fairly easy process to show the executor or administrator of her estate that he's now on the hook for the payments as the co-signer and, therefore, the vehicle needs to be conveyed to him so he can either continue making payments on it or sell it or whatever he plans on doing with it.
If he sells it, he will not be able to give a free and clear title to it to the buyer until the car loan is satisfied. So if he sells it, he must first call the loan company and get a cash payoff amount. Whatever he sells it for must be equal to or more than the cash payoff amount or he'll end-up paying some cash out of his pocket because by hook or by crook that finance company is getting the cash payoff amount... period.
It's probably worth sitting down with an attorney for an hour or so and getting proper legal advice. What happens as far as who has to pay-off the car is pretty straightforward and doesn't really require your talking to an attorney. But you don't want to mess with taking things which belong to her estate until and unless you're legally allowed to. And that's a probate issue -- one worthy of chatting with attorney about, even if only briefly.
Money owing on a car loan is still due, and payable by the estate of the deceased borrower. It's conceivable that certain loans may accelerate payments in the event the borrower dies. In any case, the executor of the estate should make payments as they become due, as with other obligations of the deceased. If a conflict develops between the executor and the bank concerning the loan, an attorney should be consulted.
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