How does Candy and his dog reinforce the theme of responsibility?

Both Candy and his dog are old. One of the themes in this book has to do with the isolation and disposability of people when they are no longer needed. Just as Candy's dog is shot because of his age, Candy feels the same way. He feels old and disposable. Candy laments that he had a responsibility to shoot his own dog instead of letting Carlson shoot it.