Got a question regarding older stolen cars

[Jeff H]

Since I'm not a detective or lawyer and I don't play one on tv, I was wondering what the legality is regarding older cars that were stolen and may suddenly resurface. For instance, say a Yenko Deuce was stolen from a dealer's service facility back in 1970. The owner was paid by his/her insurance company or the dealer's insurance company. Suddenly, that car pops up for sale today(regardless of condition). Is there a time limitation to the claim over who legally owns the car? Would the car still show up as a theft in current police records? Would the insurance company who paid the claim actually have the rights to the car? Or has time expired on any claims and anyone could buy the car and try to title it in their name? And no, I haven't found any old stolen car but doing some research made this thought pop up.