A plastic bag is a bad idea, the piggies would eat it... you either need a plastic tray or to replace your cardboard box once or probably twice a week! We have Rosewood corner rabbit litter trays that we fill with hay and the piggies wee and poop mainly in there (I am lying, they wee and poop everywhere because they are guinea pigs, but more goes in the trays than on the fleece!). Sometimes they get cardboard boxes full of hay too and they have a hay room lined with newspaper then paper bedding then lots of floor hay. If they get a cardboard box its so soggy the bottom dissolves and falls of in 2-3 days...