You do know that you can take the sliver of soap and join it to the next fresh soap bar taking its place, right?
Why save it when you can use the bar completely?
Another way is to take a washcloth, fold it in half, and sew 2 edges together to make a pouch. I would recommend adding a ribbon or something so you can hang the pouch between uses.
Slivers and remnants of soap go inside the pouch, so you can use them without them getting dislodged.
Gee. I did not know that! (insert eye roll emoji)