Dumb Question time

Yes. EA would be even worse idea if that wasn't the case.

if you buy early access they typically give you the full game as it is and you get all updates for free, eventually the entire game as it is released

There are no dumb questions only dumb answers. Yes the game will stay in your library :)

Followup question, who's got Prison Architect? Is it somewhat stable at this point? I played it a couple years back but I couldnt go 30 min without it shutting down, or walls that refused to tear down.

If it goes final ... sometimes devs abondon projects so ther is a chance you will end with unfinished crap.