When I pre wash fabric which isn't often(usually for garment making) I sew the cut edges together with a narrow zigzag or my serger then when it's washed/dried I just cut the sewn edge off. No fraying strings left in the washer/dryer and I only lose about a half inch of the fabric cutting off the sewn edge so it's worth the effort to me. I haven't yet made a rag quilt but I've used flannel for several backings and this is also what I did with the flannel.
Cari