Watch in case other shrimp get a rusty color on them. Probably not this.
If it is rust /black spot, the link above goes above and beyond offering options from natural to antibiotic medication for the disease.
These options also mention ways to increase antibacterial / antifungal elements in the shrimp tank.
It might well be a nip from fish, causing the dying black part of the shrimps flesh. Infected and turned to a place where the flesh is damaged severely.
Or very possibly different explanation of the loss of the tail as the molt caught on the tail and ripped off when the shrimp got out of the old molt. In this case if the shrimp can stay healthy enough, he might drop off the dead part in the next molt and start to regenerate the new tail. It may take a few molts for the tail to get back.
How long has this tank been set up /running?
Do you ever vacuum the substrate? I would vacuum the substrate, mainly in the front where you feed the most often to get out any muck, old food. And also vac the areas where old food might collect, dead spots so to speak.
Don't do a really large water change (I wouldn't do more than 15-20%per day) this way / vac'ing, but gradually do more sections over the course of a week.
Getting a bunch of new water in the tank too, but gradually, will help the fish and shrimp in general, a refresh of the tank. Out with the bad - in with the new fresher water.
New to FW fish? First tank in a long time or EVER??? Need some info on keeping fish?
Start here - Aquarium Advice Article
FW Favorites right now Clown Loaches, any shrimp - SW Vase Red Mangroves