I bought a mesh scrubby “bag” that has a string/bead fastener. It cost about a dollar at a department store. When I have a sliver of soap I open the end of the bag and pop it in there with whatever other soap slivers might be in there. The kids use it. It was easier than them hanging onto a slippery bar of soap when they were little.
I remember my grandmother would save them, and when she got enough, she’d make a new bar or something with them all. I think maybe she’d put them all together with some water to get them all soft, then somehow make a decent sized bar.
My wife’s family would stick them to a new bar, and so I started doing that too, and now it’s my job. It’s become almost a game, where I add a small remnant from my sink soap to the old bar from the shower once it’s small enough. But not too small, or the combined bar breaks in two.
If you don’t want to meld the old soap with the new, get the leg of a clean pair of pantyhose (one with runs/ladders is fine), or a clean sock, and put the slivers in there. Or get some nylon net (Holy Heloise, Batwoman!) and make a drawstring bag out of it, and put the slivers in there. Or put the slivers in a jar, and put some boiling water in the jar, stir it up, and you’ve got liquid soap.
I try to use them for hand soap until they’re down to a very, very tiny sliver indeed. Then they’re tossed. Alternatively, if I can find a mesh bag, I put the tiny slivers in there and let my cat enjoy them–she loves at least some brands of soap’s perfumes. It’s almost like catnip for her.