You're missing an important point - the 3850's that command high prices are AGP cards, as 3850 was one of the latest and highest performing AGP cards ever released as AGP was on it's last leg. PCI-E versions are worthless.
So if someone has an old rig and wants to spruce it up some, or maybe retro builders, those are the folks paying stupid money for a AGP cards.
EDIT: You may also have folks that need old cards for industrial applications, where a piece of valuable software is tied to a PC, and replacing the PC is not an option as that would probably cost thousands of bucks in order to configure the software anew. For example, lots of factories still run Windows XP because that's what runs their machinery. If one of their AGP cards dies, they will pay what seems to be crazy money to bring i back online, as the alternative is much more expensive.