Thanks for the input from Emma S, Nana-Up-North, Fraew, and Quilter Sue.
The fabric is loosely woven but the colors are gorgeous. It was a kit that I ordered long, long ago without being able to see the fabric. What I'm thinking is that I'll just call it done as is. My thinking is that the shredding might, just might, be stopped when it has batting and backing added. Still, it's a lot of time and so many projects to do. So I think this one will go to the trash. The fabric isn't absorbent, so no good even for car rags. Dog beds wouldn't hold up, so that's out. Really learned a lesson here. Thanks for helping me decide to do what I thought should be done, but sure do hate to waste!