These suggestions have been helpful even though I am not the original poster. I have a Log Cabin quilt that my grandmother gave me when I graduated high school. She didn't bind it...just 'birthed' it, and now those edges are fraying. I'm going to put a simple binding on it that will match one or more of the scraps Grandma used in creating the quilt. My daughter also asked me to repair a quilt that her grandmother-in-law made for them, but some of the squares (one type of fabric only) are disintegrating. For that one I plan to cut the size I need from a 100% cotton shirt and hand-sewing the replacements in. Time-consuming, yes, but a labor of love, and a project I can do in the evening.