You can fusible interfacing to stabilize the fabric so they won't stretch. Then you cut the size you need from it. The interfacing stays on the back, you don't take it off. You need fusible you can sew through and not gum up your needle. Many featherweight interfacing are available. You want very light so the quilt won't be heavy. Search online for How to make a tee shirt quilt. Not that you are making a tee shirt quilt but will give you all the details of fusing and what type.