(There is term called "knife edge" binding. It is a lot of work as it is usually done by hand. You square up the quilt and leave the last inch all around the edge unquilted. You then fold under the 1/4 inch seam allowance around the whole top. You then do the same to the back. When you have then perfect you hand stitch the two edges together with the invisible ladder stitch. You can trim the batt back 1/4 inch before you start the hand sewing but I usually just scrunch it in a little.)
I did this to all my quilts for 2 years before I learned how to bind them. I am a slow learner I guess.