How does the incident concerning Candy's dog relate to George and Lennie in Of Mice and Men?
Many people believe that the dog is a parallel to Candy. Both are considered old and useless. However, the connection between the dog and Lennie seems more apparent to me. The strongest example of which is the death of each. Does the dog's death act as a forshadow of Lennie's iminent demise? Both the dog and Lennie are loyal to their leader. The dog to Candy, and Lennie to George. George can not allow Lennie to die the same way Candy's dog did: at the hands of a stranger. He chooses to take matters into his own hands. Crooks also references Lennie's possible futre without George earlier in the novella. Crooks scares Lennie into believing that without George, Lennie would be chained up/caged like a dog. Again, this is something that George eventually realizes he can not allow to happen.
Candy allows his dog to be euthanized to "put it out of its misery" (Chapter 3), and he later laments the fact that he did not do it himself, letting someone the dog did not know well do it instead. This parallels the ending of the story, when George himself takes Lennie's life to spare him from having to experience suffering that would have been beyond his ability to understand. The two situations explore the questions of responsibility, mercy killing, and friendship, which are central to the novel.
I have a bit more to add to the previous answer. Candy believes he is becoming useless, just as his old dog is no longer the functional being he once was. Candy fears that once he is no longer of use to the ranch, he will be tossed aside too.
Candy's worry is one that all of the men who earn their living manually fear, even George and Lennie, who dream of the Utopian paradise that will save them from similar fates.
Also, John Steinbeck specifically writes something suspicious.
Notice that when Candy walks in the room (ch. 3) he says he has a gut ache. What happens when someone's stomach aches? They may have gas, which smells bad obviously, and is caused by turnips in this case.
Then, Carlson walks in the room and instantly smells something. What could it be? The dog, or Candy's gas?
***Why would Steinbeck put something like the gut ache in? Randomly, I doubt it. Before this, the dog was useless, but never smelly. It may be Candy's fault for not speaking up, saying he had gas. Similarly, it may be George's fault for Lennie's death. From the incident in Weed, it is obvious Lennie is dangerous, and George should have been keeping a closer watch on him. When Lennie killed Curley's wife, George was outside playing. ***