It seems that Crooks' dreams die because of the racial segregation that isolated people of color from others. Steinbeck uses Crooks to display how the economic challenges experience by Americans during the Great Depression were worse for people of color. For poor White Americans, at least some level of bonding or solidarity could be evident because of their impoverished condition created some link of commonality. However, I think that it is important to understand that Steinbeck suggests that people of color faced another hurdle in their predicament during this time period. They were marginalized on both issues of class and race. In the competition for jobs, White Americans were going to win out and people of color, if even in competition, would be secondary, at best.
For Crooks, this is where he is. The need for companionship and the mere notion of sharing life with someone else is of vital concern to him and it becomes the reason that his dreams have died:
"You got George. You know he’s goin’ to come back. S’pose you didn’t have nobody. Sure you could play horseshoes till it got dark, but then you got to read books. Books ain’t no good. A guy needs somebody - to be near him.' He whined, 'A guy goes nuts if he ain’t got nobody. . . . a guy gets too lonely an’ he gets sick.”
It is here where Crooks' dreams have died a painful death. Crooks understands that he is not going to experience any companionship, being a victim of both the economic state of affairs that often precludes such attachments because of the need to find and keep work. He also knows that the racial condition of segregation will keep him isolated and separate from others. In the end, this is where Crooks' dreams of solidarity and some level of human attachment live and die. It is for this reason that there is only a flicker of hope whereby some level of attachment is evident when Candy and Lennie are both discussing with him their dreams. Yet, the end of the scene is one where Crooks is left again, alone. This ends up being the representative of statement of Crooks' dreams and their death.