Fleece isn't supposed to ravel either so it might be a relatively safe type of cloth. I did some more reading on happy huts and found out that there are several types of problems that can occur.
1. Long loose strings of shredded cloth that the bird gets tangled in.
2. The bird picked out the stitching that holds the pieces together and made a long thread that way and got tangled in it.
3. The bird chewed a hole through the cloth and got its head stuck in it.
4. The bird ate the fuzz or cloth and died of crop impaction from the fibers.
5. A toenail got caught in the cloth or the stitching and the bird was injured trying to pull free.
This website has some reports:
http://www.pine4parrots.co.uk/Pages/Hap ... rning.aspxIf you want to use any kind of fabric, the safest thing would be to only have it in the cage when you're in the room and will know if there's a problem.