Do they sit there? Do they eventually get deleted? Do they get put up for adoption after a certain amount of time?

I'm pretty sure they just sit there on the account.

They just sit there. They used to have the names come open to use but with the newer naming system that's not even a thing anymore. And ages ago (like 5+ years ago) they used to delete longer inactive/frozen accounts not labeled for a deceased user. But that was rather time consuming and would result in the site down for a day or two. With not deleting it does allow people to come back because many of us life happens and we can't play all day like we once did.

LOVE your HA, had to ping to say that :)

Also wanted to add... I'd pay real actual money just to see my original account from 2004 >_< I miss all my old friends, pets, I don't even recall what my username was though truthfully.

Dude I too had an account way back in 04 before the bot ate people. I did come back in 05 when the site did but stopped playing. Sadly once data is deleted like our old ID and such there's no recovery :( which I think is why they originally moved to simply allowing names to open up and be claimed and give the old player a free rename. Now the only thing that can be nabbed is our usernames should we not play long enough.