If the 'tub' needn't be solid, as in the cage itself is dimensionally stable enough enough without the 'tub' but lacks some other quality, like resistance to liquids, then you might try shower pan liner material. This is thick, typically almost 1/16" thick, PVC plastic. It comes in 48" width, is sold by the lineal foot and are cut from a roll so you can get as many feet length as you like.

The idea would be that you buy it perhaps 8" or 10" longer and wider than the cage and allow it to run up the walls of the cage in both directions. You could either try folding the corners, perhaps using a binder clip or clothespins to hold the fold, or you can cut, fold and glue it permanently into shape. Supplies and instruction for doing this are available where you buy the sheeting. I have cut and glued it and it isn't hard once you get the hang of it. In effect your making a making something like a fitted sheet, like for a bed, out of heavy duty plastic.

If you go with it flat with folded corners it would be easy to store, you could roll it up, and clean.