All inquiries about the debt should be referred to the estate. It is not up to you to sort out or decide whether or not payment should be made - indeed it would be very improper to do so without the permission of the estate and because probate has not been completed. Remember, the estate, not you, legally owns and is responsible for the car.
They should not be seeking money from you or your family and if they are, this would be regarded as illegal and unethical practice - should be reported to the financial regulator.
My advice would be to write back saying the person who owes the money is deceased and give details of whoever is the Executor of the estate. Alternatively, you could pass on the requests for money to the Executor and get him/her to deal with it (as this is their function). If they persist on contacting you, set the financial regulator on them.