MAD Magazine suggested something like this back in the '60s. Their gripe was that that little piece of soap you get at the very end is damn near useless so why not make soaps with a hollow center. The thinking wasn't all that great though since that means you just get a collapsing smaller piece quicker.

How 'bout a little sink the size of a lunchbox with sonic dohickeys. You put your hands in the water and sonic waves clean the beejezus out of your hands? Sure, maybe you'd have to crank up the power to make it speedy, but safety be damned!

:)

I have seen a small bag made of net which can be used to contain soap ends so that several pieces can be stored and then used as a single soap source.

I don't get bothered by useless soap pieces anymore after I started using one of these http://www.leafa.com/

When my soap gets too small, I get out a new bar and use it. When I'm finished with my shower (or hand washing or whatever) I press the old sliver of soap on top of the new one while it's still wet. By the time I return to use it, the soap will have dried and the sliver will be permanently welded on.

FYI, Leafa sells a bath mitt for bar soap.

Have a bar of soap with a suction cup attached or a semi-circle cut out of one end so you can stick it to a bathtub wall, shelf, or washcloth rac.