Welcome from Ontario, Canada. It could be natural handmade quilt batting. In vintage quilts before manufactured batt were available, you had to card your own cotton and lay it out in a solid layer and then quilt. The bits that you see may be part of the cotton ball husk. As for fixing it, you could take it apart and reuse the top with a new back and batting. If that isn’t something you want to do, it can still be folded and put on display.