Like his dog, Candy in "Of Mice and Men" is old and has nearly out-lived his usefulness. The dog's death is suggestive of what will soon happen to him--he will be discarded by society.
The skinner [Slim] had been studying the old dog with his calm eyes. "Yeah," he said. "You can have a pup if you wnat to." He seemed to shake himself free for speech. "Carl's right, Candy. That dog ain't no good to himself. I wisht somebody'd shoot me if I got old an' a cripple.'
Candy looked helplessly at him, for Slim's opinions were law....Candy looked for help from face to face.
Candy is alone in his anxiety. For, as George says, "Guys like us, that work on ranches are the loneliest guys in the world. They got no family. They don't belong no place...." While George has Lennie to give his life some meaning against the terrible isolation of his state, Candy has his old dog. But, when Carlson takes the dog and shoots it, Candy is bereft in a group of isolated misfits.
Steinbeck's theme of the interdependence of society is one that he explores throughout the novella; one method that he uses is to show the negative effects of isolation as exemplified in the episodes of Candy and his dog.