I have a different perspective on my "use" quilts and accept that they will slowly fall apart especially as often as I wash them. I designate some for the idea that they will slowly disintegrate in the dog basket after their human time is done. So my answer is -- it depends.
For a quilt where the fabric on one side or the other isn't holding up well, I will recover which ever side with a happy fabric and either do some practice quilting or a basic grid of some sort. Typically I'll just cut off the old bindings and replace with new at the same time. I am facing the decision of what to do with a quilt I made my husband before he was my husband (so more than 20 years old). Have already put on a new back and redid the binding. Now some of the top fabrics are having issues but the back is holding strong... I think my answer is to make a fresh one for him and this to go on the sofa or something without further repairs.
One of my dogs (now passed) was a chewer. He ate many things from socks and underwear to holes in quilts, some quite large. For such times when a patch is required, I now just applique a heart shape on both sides big enough to cover the hole, adding some batting if needed. Doing it by hand means you don't even have to match the fabric shape. Sometimes bright red and sticking out like a sore thumb, other times (like when I do them for friends) coordinating with the fabric. Typically this sort of quilt is being used to protect a "good" quilt or is between layers and not seen -- so the bright/non-coordinating fixes aren't such a big deal and better than having your toe (or entire foot) land in the hole.
I miss Buddy. He was a true rescue, not just rehomed, and had a hard life before he came to us. Honestly he wasn't that great a dog. But he was my dog and I loved him more than my quilts. Our current dogs came to us because Buddy was so bereft after he lost his bonded dog companion, they were more his dogs than mine. He needed a pack and our current dogs needed a pack leader when their original daddy died, it worked out well for the time he had remaining.