Dying or molting? When they molt the shell that grows on the upper body (claws, head, to mid-torso) sheds. The remains can look like "half" of the crab.
They don't necessarily die if they don't have a new shell to move into (ie snail shell) - they can go around "naked" although they are vulnerable to predation in that state.
We once had a HUGE hermit that somebody 'donated' to the shop that was too big for the largest shell we could find. He lived in our sump a while, 'naked' until Scott put a 1" PVC elbow in - he hopped into it quickly and wore it around for ages! Looked funny but it did the trick.
So yours could just be molting - take a close look at whatever remains you are seeing.
Jenn
