Candy is old and has only one functioning hand. He worries that he will soon become relatively useless as a worker on the ranch. This is why Candy is interested in George's and Lennie's dream of owning their own farm. Knowing that he can not be useful as a rancher for much longer, Candy offers to contribute money to Lennie and George so that he might join them on their own farm.
Candy's dog is similar in that he is old and useless. Candy eventually allows Carlson to put the dog out of his misery. Candy recognizes that, just like his dog, he can become obsolete.
He said miserably, "You seen what they done to my dog tonight? They says he wasn't no good to himself nor nobody else. When they can me here I wisht somebody'd shoot me. But they won't do nothing like that. I won't have no place to go, an' I can't get no more jobs. I'll have thirty dollars more comin', time you guys is ready to quit."
Candy clings to the idea/dream of joining George and Lennie on their own farm, as if it is his last hope. When Candy and George find Curleys' wife dead, Candy seems to know that the dream is also dead.