The character in John Steinbeck's novella, Of Mice and Men, who "has one hand and is very old" is Candy.
Candy is an old ranch-hand who lost his hand in a farming accident. Given his disability and his age, Candy worries about his future with the ranch. The symbolism which surrounds Candy's lost hand is very important. Given that Carlson's desire to shoot Candy's dog had to do with the fact that Carlson found the dog useless, Candy feels as if he too may be found useless and be "put down" as well.
Candy's age also feeds into his feelings of insecurity--with himself as a man and his ability to perform as a proper ranch-hand.
Essentially, Candy's defining as an aging character with a disability is important when one examines the deeper meaning of Candy as a character "who has one hand and is very old."