Thrifty folks learn to meld the sliver to a new bar of soap. It takes a few days sometimes, but eventually the soap remnant will adhere to the larger bar. Press them together while they are wet.
Step2
One suggestion is to slit a sponge and insert the soap into the center. There are products for this very purpose (to contain a bar or bits of bar soap).
Step3
Soap Art
Collect the slivers of soap and make an art project from them. If this doesn't appeal, send them to artist, Jill Greenburg, for her art work. Collect together all the soap slivers and mail them to Other Leading Brand, 93 Bright St. Jersey City, NJ 07302
Step4
The sliver of soap can be broken into bits and put into a liquid soap dispenser. It should soften and a little water added to the solution will help it dissolve into liquid form for use.
Step5
Grind up the slivers of soap and mix with oatmeal in the blender. Add a little oil and water, then press it into soap balls. The exact directions are in the link below.
Tips & Warnings
Don't just keep accumulating the bits and pieces under the sink. They need to be used up somehow.