If it passes through Tesla in any way (auction is usually a red flag) there has been cases that FSD gets removed a while after the auction finishes. It always involves a dealer buying a Tesla at an auction (where Tesla is the seller). Tesla likely sold the car for cheaper at the auction with such features removed (in the cases so far the dealers don't have paperwork from the auction that promises that FSD would remain, sometimes they have the original Monroney sticker but that's largely irrelevant).
Private party sales avoid this.
Long thread on this:
Tesla removing FSD from third-party dealers
You will see conflicting accounts in that thread. One that claimed a Tesla rep says that any car that passes through a third party dealer will get FSD/EAP removed (regardless if it passes through Tesla hands or not). Note in that case, the dealer (Carvana) did not advertise the car as having EAP (so they probably knew something the buyer didn't) and buyer bought it knowing that.
Then later in the thread someone bought a car that had FSD from a third party dealer and was able to retain it (car was bought from a private party by that dealer, not an auction). Dealer said Tesla rep says that as long as the car doesn't pass through Tesla hands, FSD/EAP does not get removed. So there are conflicting accounts depending on which rep you ask.
There are other cases, where Tesla does an "audit" on an ownership change and this may remove certain features (sometimes by mistake, sometimes on purpose if it is a case where Tesla ever had their hands on the vehicle).
