foundation piecing you do not use paper---you use a fabric foundation instead- sometime muslin- sometimes an interfacing of some sort---and you do not have to remove it-
i do 98% of my paper piecing on foundations (usually muslin) simply because i hate removing paper- it does add an extra layer of fabric to your quilt- so makes hand quilting a bit more difficult- but if you are machine quilting it doesn't make much of a difference- does add weight to the quilt.i use all sorts of (cheap) thin fabrics for foundations- generally fabrics i do not think i would want to use for piecing but would be ok as a foundation-
i've even done some foundation piecing right on batting- --- kind of a quilt as you go result.