Chapter I of Of Mice and Men offers an interesting description of both Candy and his dog that shows them as parallel characters. Their description also serves to foreshadow their role and their potential time-line within the novel.
The old man came slowly into the room...And at his heels there walked a drag-footed sheepdog, gray of muzzle, and with pale, blind old eyes. The dog struggled lamely to the side of the room and lay down, grunting softly to himself and licking his grizzled, moth-eaten coat.
Here we see the correlation that is made regarding both, the man and the animal, being old and slow. These words also suggest that, like his dog, Candy may very well be getting to a point in his life where his age may render him useless, or even lame. In more that one occasion it is well-implied that, since the dog is so old, so is Candy. After all, this very old dog has been his company since the dog was a puppy.
The dog is a cripple, smells bad, and seems to be a disturbance to some in the ranch. This is why Carlson volunteers to "put the dog out of his misery" and shoots the dog in the back of its head. The dog was alone in this world, and overshadowed by the birth of Slim's cute puppies. Similarly, Candy is alone in the world and also overshadowed in a way by the younger and more able farm hands.
Also, Candy confesses to George and Lennie how he is also considered old enough to be sent away somewhere. This is what prompts his idea of joining in with George and Lennie in the attainment of their ultimate dream: to have their own ranch together.
Jus’ as soon as I can’t swamp out no bunk houses they’ll put me on the county. Maybe if I give you guys my money, you’ll let me hoe in the garden even after I ain’t no good at it. ... I’ll be on our own place, an’ I’ll be let to work on our own place.
These words are also indicative of a loyal person. Candy is willing to be loyal to the cause of George and Lennie. With his actions, he also demonstrates that he is willing to always remain by their side. This is another characteristic that he shares with his dog, who was his sideline companion for its entire natural life.
In the end all three, Candy, George, and Lennie, lose the dream bitterly due to Lennie's accidental killing of Curley's wife. After this, George mercifully kills Lennie to avoid a cruel and vicious killing by the hands of Curley. Yet, Old Candy remained, until the end, a loyal and faithful companion of George and Lennie.