My great grandmother made me a quilt that had wool coats & left over upholstery fabric in it!
I won't go that far but I have used old blue jeans cut into squares, sheets--cotton & poly/cotton, flannel, extra wide cotton, and double sided pieced cotton. Bearding is usually a problem with the batting--not the backing fabric. If it came through poly/cotton--it would have poured through muslin. Sheets are actually more tightly woven than most quilt shop quality cottons. Even the cheap sheets are 150 thread count whereas the best quilting cottons are less than 100. The main problem with using sheets is some types pill so there will be little nubbies but some muslins pill, also and due to the higher thread count, they are harder for hand-quilters to quilt through. Some threads and/or quilting machines may not like the tighter woven sheets either but can usually be coerced to play nice.