I don't know if they still make em, but you're probably thinking of "the scene machine," from "Virtual Backgrounds" or, I think the older name was "EPS" (Environmental Projection Systems).
There's probably a lot of them sitting around in back rooms somewhere, or for sale online. Something you should know, though, is that they're basically useless without the special background. It's a special material, called a high-gain retroreflecter, with a gain factor on the order of five hundred or a thousand times (meaning that it is seen, by the camera, as being that much more reflective than white paper). So if you try to buy a system, make sure it comes with a clean, undamaged screen. Fwiw, the backgrounds themselves cost roughly a couple thousand US dollars back in the day. You won't be able to buy a "proper" new screen elsewhere, to the best of my knowledge.
These were pretty incredible systems back in the day; I think the advent of digital imaging, with dirt-cheap chroma-key backgrounds mostly displaced them. Best of luck.
Ps, the black screen you recall was something that EPS stretched out an inch or so in front of the retroreflector. It helped to get darker blacks in the projected image in bright ambient light.