small cut fleece used as bedding?

I am a new rat owner that is using paper bedding. That is going to get a bit costly and a little impractical, so I was trying to come up with more cost effective ideas. Fleece sounds good because its soft on the rats feet and its washable but my rats like to dig and play which the paper bedding is good for. so if I were to get a large fleece blanket or jackets and cut them into paper bedding size pieces would that work? There are a few issues that I can think of like washing not getting the fleece all the way clean or it could be a choking hazard if cut too small but on the surface this sounds like the best of both worlds. Can anyone tell me why this would be a good or bad idea? I'm going to stick with the paper bedding for now because I don't want to potentially harm them.