Most stories don't have "meanings" in the sense of some simple moral that you are expected to take away. Instead, the point of fiction is to explore the ways in which imaginary characters act and react in imagined circumstances, sometimes purely for the purpose of entertainment and sometimes as a way to understand some aspect of human nature.
In the story “Looking for Mr. Green,” Nobel Prize winning author Saul Bellows explores issues of social class and intellectual traditions. The first situation he uses to explore this is that of members of the middle class who lost their jobs during the Great Depression, and either became unemployed or underemployed. This change in financial circumstances leads the protagonist, George Grebe, a professor of Classics, to take a job at a welfare office. His new position brings him into contact with people living in extreme poverty who lack his degree of formal education.
In his new position, Grebe needs to confront the problem of identity, not just as a philosophical issue in the more theoretical tradition of metaphysics and philosophy of language, but also the stark ways in which money and social class shape identity. In a sense, one could say that the story argues that poverty forces people to become Marxists.