The Real Ghostbusters/WMG

The Doomsday Door in the episode Knock, Knock is actually a Containment Unit
The Ghostbuster themselves seem to have no other manner of getting rid of ghosts other than putting them into the Containment Unit and on various occasions there have been the problem of what happens when all the ghosts get out of the Containment Unit at once and it's not too dissimilar from what happened with this door. It seems like the Containment Unit would have to be kept intact for the rest of time, leaving a problem of how to warn future civilisations. It's a problem that comes up in nuclear waste disposal and it seems to come up with the warning stone and the door itself which says "Do not open until doomsday"
 * That makes sense: perhaps the realm behind the door is a pocket dimension that some ancient civilization conjured up to banish the ghosts plaguing their era. It'd even explain that Nightmare Fuel scene of a skeletal boat captain laughing and ordering his human slaves to keep rowing. Maybe some of the people who created the door got trapped inside when they sealed it shut the first time (just like Egon thought was going to happen to them), and they've been at the ghosts' mercy ever since.

The Stay-Puft Marshmallow Man was recreated inside the Containment Unit
The Ghostbusters never "caught" him in any normal sense, but he's inside the containment unit in the cartoon, and somehow he's turned friendly now that, according to Ray, he's not being controlled by Gozer. But how's that possible, and when did it happen? Well, the Destructor was formed by all the PKE energy Gozer had gathered in New York and, when Gozer was dispelled, that energy got released again (causing Stay-Puft's physical form to collapse into marshmallow goop). Then that shapeless PKE energy gradually spawned dozens of individual ghosts, which the ghostbusters hunted down and caught in separate cases over the next several months. Once the last ghost was captured and sent into the containment unit with the others, they all merged back together into the Stay-Puft Marshmallow Man... except, without Gozer's influence, he now has the same friendly personality that Ray imagined he'd have. He's probably also a lot weaker now than he was as the Destructor, but he's still big, strong and benign enough to make him a useful last-ditch option against other ghosts.
 * His being weaker now than he was in the movie, and being a pure ectoplasmic ghost rather than a walking, corporeal marshmallow giant, also explains why they can use a trap to release and recapture him. He's not so much the Staypuft Marshallow Man as he is the "ghost" of it.
 * There was an episode that explained it in flashback, IIRC it was them telling the story to a reporter of how Slimer became their Team Pet, after killing Gozer they went home, took off there marshmallow covered jumpsuits and tossed them in a box in the basement, where a leak from the containment unit caused the gunk to reform into the animated version of Stay Puff, which they busted, trapped, and stored.
 * It formed into Evil Twin versions of themselves rather than Stay-Puft, since the PKE energy took its form from their latent auras. Still, it shows that the Gozer/Destructor PKE energy stayed around after they defeated Gozer, just formless and unchannelled again.