The most evident of the similarities between both situations is that one in each must die. Candy lets Carlson shoot his dog when the old canine is no longer of use and when others fail to support the dog's ability to live. Candy lives with the guilt of letting someone else kill something that he loved so much. In much the same way, George is forced to kill Lennie rather than let others kill him. Both Candy's dog and Lennie are shot away from the eyes of others. One can even argue that both Lennie and Candy's dog are unaware of what is happening or going to happen to them, as Candy's dog really does not offer much in way of resistance when Carlson approaches him and takes him out. Lennie's last words the leave his lips are the vision of his future and the farm that awaits him. Both George and Candy are filled with an immense emptiness after their companion leaves them. It is for this reason that Candy is so insistent on joining Lennie and George. It is also for this reason that George appears disconsolate at the end of the novella, besides himself with a sense of loss that underscores the pain of what it meant to lose someone so close.
The most evident similarity is the fact that both Lennie and Candy's dog provide companionship to the men to whom they are attached. Lennie shares a very close relationship with George and provides him with comfort. Because of Lennie, George—unlike the other men on the ranch—has someone on whom he can rely and with whom he can communicate. Lennie is a trusting and trustworthy friend who will always be there for him. Candy's dog provides his owner with the same kind of friendship and security. Even though the animal cannot respond, as Lennie can to George, it has the same attachment to Candy and gives him the comfort that he at least has something that the other ranch hands lack.
In both relationships, one is a caregiver while the other is the receiver of such care. George looks after Lennie and is his mentor. Lennie depends on him to find them jobs and to act in his best interests. There is a relationship of trust between them. Candy has been tending to his dog ever since it was a puppy. He has provided for it, and it apparently trusts him. In both instances, though, that trust is betrayed. Candy gives in to pressure from Carlson and allows him to shoot the dog. He is led to believe that it is in the best interests of the animal that it be shot. George, likewise, believes that it is to Lennie's advantage that he should kill him at the end of the story. He wants to protect his friend from Curley's vengeance and brutality.
The animal imagery Steinbeck uses to describe Lennie also likens him to an animal. Lennie is intellectually disabled and has poor judgment. He cannot always fathom the outcomes of his actions. One can say that, in this regard, Lennie can be seen as George's pet. The relationship between the two men is akin to that between a caring owner and his charge, just as it is in the relationship between Candy and his dog.