Yes, ghost shrimp can live alone. Ghost shrimp don’t need to live in groups and a single ghost shrimp can thrive on its own.
Just make sure it has plenty of water to swim around. You can keep up to four ghost shrimp for every gallon, but that doesn’t mean you should confine your lone ghost shrimp in a tiny 1-gallon tank. A 5-gallon tank is the bare minimum requirement for ghost shrimp, regardless of whether you’re keeping just one or a bigger colony.
With that said, if you’re keeping ghost shrimp to help keep your tank clean, a lone ghost shrimp wouldn’t be enough. For example, you may want to keep at least three to five shrimp in a 20-gallon community tank.