There are very key elements to answering this question that are left out from our description. For example, did Grace offer for Vern to keep the old parts of his car after every part was replaced? Or did she simply keep the parts without asking? In a normal situation, the mechanic asks the owner of the car if they would like to keep the piece or not. If this happened in Vern’s situation, then the answer is much clearer.
If Grace asked Vern whether or not he’d like to keep the old parts of his car and Vern said no, then he’s given up ownership of the parts and whatever Grace would like to do with them. They are no longer ‘his’, and if Grace keeps them all and makes a new-old car out of them, then it still doesn’t belong to Vern. His Volvo would be the one comprised of the new parts, which he paid for each time, and we live in a world where ‘If I pay for it then it’s mine.’
That would mean that the Volvo itself changed with the first new piece that Grace fixed. It was still Vern’s car, but it was Vern’s Volvo enhanced version. But the second that Vern turned down the old part, he gave up any claim to it, and therefore the heap of parts cannot be his car.
However, if Grace never offered the old parts to Vern, and simply kept them without telling him (which is a little creepy when you think about it too hard), then ownership still belongs to him. Those parts belonged to the original car that Vern signed off on at the dealership years ago, and he paid for those parts. Not directly, but they came with the car that he paid for on a whole.
Well, if Vern never offered up the parts of his car, and still bought new parts, which car is 'Vern's Volvo'? The car he drives. He paid for each part, and that created a new vehicle of new parts. It belongs to Vern, because each part belongs to Vern individually. The parts that are in Grace's garage that she's been collecting are just pieces of an 'old' car, but not it doesn't make up Vern's car. All the parts are there, but the whole is greater than the sum of it's parts. Vern doesn't drive that pile of car parts. He doesn't use it on an everyday basis, and it's not practical to him. The car of new parts is his car, just not in the same condition as when he originally bought it.