You wouldn't keep anything out of the bedding and tray, you'd put everything in it just like you normally do on the bottom of the enclosure. It would basically just be a removable bottom to make it easier to dump and wash, instead of having to scoop everything out. A liner of sorts, I guess you could say.
I can dump a 20-gal aquarium, but it's big and awkward to dump into a garbage bag, stuff gets all up and down the walls, and hung up on the lip at the top. Washing it out is a pain, too, especially in the winter when I can't go out and use the garden hose. Imagine a front-opening enclosure of about that same size, with something like a boot tray on the bottom but with slightly steeper sides. Put tray in enclosure, then put bedding, furniture, animal in tray just like you would without the tray. To clean, you still have to take out the furniture and the animal, but then you can just pull out the tray and dump it, even wash it at the sink or in the bathtub, without having to maneuver the whole entire enclosure. Make sense?