A hamster may lose a limb due to accident or genetic deformity. If a hamster loses a limb due to accident the wound will need veterinary treatment to avoid infection.
If the hamster is missing a limb due to genetic deformity it should not be bred from as the deformity can be passed to offspring. Also the mother and/or father which passed the deformity should not be bred from again.
A hamster with a missing limb will adapt and cope surprisingly well.