Cloth that does not unravel the yarn and such - Kinda off topic!

[axelah]

Okay, well maybe a lot off topic...
But you ladies seem to know a lot about cloth and I could go to a bird community and ask but lots of them do not use cloth or know extensively about cloth! You can direct me to another community also lol.

I want to use cloth for the bottom of my bird cages instead of paper. I use old terry towels now but with the bird's claws and when they bite at it, the stitching becomes loose and it unravels and such. It's dangerous for the birds.

What cloth does not unravel and will not bring about those loose "loops" and such? The cloth and the stitching should stay nice and taut.

I was thinking flannel? But flannel pills, right? Not sure if they can catch their nails in that or eat that fuzz.
I was thinking plush or fleece? I know fleece is used for guinea pig liners but I was hoping for something that I could just use 1 layer which did not unravel and was absorbent.

Thanks SO much! xoxo if this is inappropriate please just tell me!