With ghost or red cherry shrimp their shell gets a little white before molting. They look sick but this is normal.
Now the following I have personally seen. Crayfish molt by laying on their side and slowly scooting out of their shells. They feel like rubber and are very slippery right after they molt.
RCS molt by bending into an upside-down "U" shape, then jumping out of their shells. It's so fast, first the shrimp is there, then *BAM*, you see an empty shell.
For bamboo shrimp I'm not real sure. I just end up finding a perfect shell the next morning, cracked open at the top of the thorax.
The detail is astounding and many newbies will think they found a dead shrimp.
Shrimp and crayfish will often eat their shells to recover the calcium. If they don't eat them within 7 days I remove the shells from the tank. But you should leave the shells in there to give them a chance to get the calcium back.
Shrimp and crayfish, because they are so soft after molting, are very vulnerable to attack so that's why it's critical that they have a hiding place. It takes 4-8 hours for a 5 inch crayfish to harden up after a molt. Smaller creatures may take less time.