I don’t think FSD beta is the concern but FSD for the OP. From what I heard here as soon as dealers or auctions make the purchase from previous owner and sells to a consumer private owner, FSD is removed. I wouldn’t even chance it as 12k value unless the dealer is willing to guarantee. There has been several post here every time it was sold private FSD was transferred while license dealers triggers Tesla to delete it.
Actually, I'm pretty sure I've heard the opposite.
First: There's the FSD subscription, where one pays for FSD on a month-by-month basis. And there's the bit where one buys the FSD option, as in forking out (these days) ten or twelve grand, and one has FSD in perpetuity. That's what I have. The below is about this bought FSD option.
Case 1: Somebody has a Tesla with FSD. They trade it in for a new Tesla at a Service Center. The car is now in Tesla's hands, Tesla (importantly) has the title: They remove FSD, and sell the car without it. Their prerogative, the buyer of the used car
knows that it doesn't have FSD.
Case 2: Somebody has a Tesla with FSD. They walk into a non-Tesla location (Car Max, a Ford dealer, whatever). They sell the car
and get money for the car with the additional value of the FSD included. Car Max, the Ford dealer, whoever, has the title, sells the car to a new owner, with the knowledge that the car has FSD on it, and the new owner forks over the value of the car, including the FSD option.
In Case 2, if Tesla comes down from on high at some point and removes FSD, that's theft, and no two jokes about it. Unless Tesla
pays the new owner the value of the FSD they just removed. Which Tesla has never done.
Now, a couple years back, there was a big kerfuffle. There were several people, maybe a dozen? Who did the back end of a Case 1 and bought a used Tesla from Tesla. The problem: Tesla had been planning to remove FSD from these cars but forgot. So, they came down
after the fact and removed FSD when the cars were in possession of the new owners. OK, so maybe the cars weren't priced as if they had FSD on them. The new owners were delighted with their new purchases and were happy to have the FSD. Losing FSD like that got them to the point where steam was coming out of their collective ears and the next thing you know there were articles in online places like Ars Technica, Tesla Forums everywhere, and it was getting into dead-tree publications.
It wasn't exactly like Tesla was.. doing something.. wrong, except that they got the timing of all this with the removal
after selling those FSD-equipped cars very, very wrong. And the lawsuits, they were a'coming. And Judges and Juries can get very picky about stuff getting removed from sold objects after the fact, be it software or no, be it advertised or not. So, Tesla blinked first, restored FSD to
that selected group, and that was that.
Far as I know, that's the situation. If the OP bought the car from somebody, and the chain of ownership didn't involve Tesla (and that means: If the Tesla in question is owned by, say, CarMax, and CarMax takes it to a Tesla SC for a tune-up and general check,
Tesla doesn't own the car and should not be removing any FSD options), then the FSD should stay on the car.
Now, if Tesla showed up at an auction, bought the car, buffed out the dents, removed FSD (it's their car at that point), then sold it at auction again, that's their call to do that. When they have actual ownership of the car. Otherwise, no.