I regularly use ripped-up bedsheets as foundations for my crazy quilts. I learned that from my grandmother. Neither her 50's-era machines nor my modern machines have any problems sewing through them. I stitch scraps down to the foundation (sheet) square, and then add decorative stitches over the top - zero problems.
The extra layer does add some heft to the finished quilt but that's what I grew up with so it seems pretty normal to me.
