Fleece cage liners frequently have an absorbent layer in the center to soak up pee. They can be tricky to fully dry in a machine, but they do wear very well. I've never tried fleece as shelf guards, though I do have a cover for the cage that's also made of fleece just to stop any drafts.
For furniture, my guy has both a fleece hammock from ForCHINate Chins and a fleece tube from... somebody else on here (Michelle?), and he seems to split time equally between them and his stone ledge from Chin on the Rocks... when he's not on his Flying Saucer.