The sale of a car

Actually, if it's prepared properly, a promissory note (an i.o.u.) is a perfectly legal document, of a type with a very long history.  And, again if it's done properly (the motor vehicle people might be able to help you with this one), the note can be used to put a lien on the title to the car;  if necessary, you could repossess it.  This is a much better solution than keeping title to the car, because if your mother does that, she would have to keep the insurance on the vehicle and she could be potentially liable if the aide causes an accident.

If your mother passes away before the note is paid, the note becomes an asset of her estate, just as the car itself would have, and it can still be enforced, either by the estate or by whoever gets the loan as part of their inheritance.