The symbol of having a farm with all that great stuff gives lennie and george hope for the future.
"An' live off the fatta the lan'," Lennie shouted. "An' have rabbits. Go on, George! Tell about what we're gonna have in the garden and about the rabbits in the cages and about the rain in the winter and the stove, pg16
"Carl's right, Candy. That dog ain't no good to himself. I wisht somebody'd shoot me if I got old an' a cripple." pg 67
The way in which Carlson kills the dog—with a gunshot to the back of the head—foreshadows Lennie's death and likens Lennie to Candy's dog: they're both powerless, innocent, and doomed.
me either, i wouldn't want to live in a time like this all weak and old.