On any given production, a ton of people have to have access to the script. Outside of production, scripts are handed over for various purposes, including promos, archiving etc. And then there are business like The Black List which are primary source of not originally (studio) comissioned scripts.

Form what I've seen, ONCE the material's out / production over, not many fucks are given if the script is out there as well. Now, is it legal? Who knows, depends where it came from probably. Heat would be on if it's a script in or before production, but it also varies.

I don't know how people get screenplays originally, I'm just searching and organizing ones that are freely available online already.

I also wonder if the producers make the script available to anyone?