It's a stropping handle. It probably goes with the razor head, but not the handle (also the case doesn't go with the head, either). It would go on the end of the original handle and you'd put the blade in the slot and you could strop the blade on your razor strop. The two cases aren't intended to fit together. Probably one for sharp blades and one for dull.
Originally Posted by Ray Surburn
This is neat stuff!
Brevity is the soul of wit.