I have personal experience here. My car got stolen and I got the insurance payout then a few months later, police called to say they’d found it. I told insurance company and they collected it.
A month later, the new owner sent me a letter asking for spare keys so obviously insurance company sold it on legally.
You speak more truth than you know. 
Well the insurance company definitely owned it after paying you out. If you had a right to claim ownership, you could, but because its not automatic. Its just that the insurance policy , or law, says they must transfer ownership to you if you want, and repay of course.
There are numerous examples of the “stolen item reclaimed decades later” in the auto’s…
eg see
http://www.proctorcars.com/incredible-stories-stolen-cars-found-decades-later/
In another case, a poor VW kombi van restorer had found a wreck, totally just the shell, fully restored it, and then when the vehicle was being exported, VIN came up as stolen, authorities sieze it, and say they are returning it to the owner from the time of the theft. (insurance company .)
Well hang on, he found/bought a piece of garbage , for which he would not need to do paperwork, and he could have bought one of a huge number, which are identical to him, and then he puts in all the parts ,engine, seats, windows,everything except the shell, and does all that work, and then they say he doesn’t own any of that any more ??
I understand that the common law said that cases where title was said to have been actually handed over by the owner were final , because otherwise a vexation vendor could interfere with the new owner, eg reclaim the goods from a built house, or working car, or interfere with the new owners business in some way, even before the end of the court case… the court case could have been used for causing duress as much as it was about asking for reparation from duress. And that people who received special items would have to return them, because while they could not be said to be the thief, they could know they were stolen , if they were obtained cheap or from irregular source.
But it seems absurd that in the case of a very degraded vehicle being restored by an innocent third party, you’d think that the degraded vehicle would have been thought of insignificant part of the restored (re)incarnation.
Let’s say I’m the other end of this. I go out and buy a used car from a reputable dealer. I have insurance on my car.
A few months later, it is discovered that the car I bought had been stolen at some point. This was unknown to both myself and the dealer I bought it from. The insurer had paid the owner of the car when it was stolen so they now own the car. They show up and take my car.
Do I have the basis for putting in an insurance claim for my now lost car?
I think in that circumstance the restorer might well have a claim for restitution/unjust enrichment, to be repaid for the expenditure and effort he put into enhancing the value of the originally crappy asset. Which, in effect, would be a claim for the full value of the restored vehicle, or as near as dammit.