The Underclass Question

Is there a black underclass? If so, how large is it and where does it or does it not intersect with the folks that Cosby admonishes?  How do we use the term and what do we mean by it?

By underclass, I would mean a dynamic set of people who are socially indigent. That by their behaviors and beliefs, that by their lack of assets, both personal and material, that they are fundamentally incapable of upward mobility in American society.