Moving takes money - money for the physical move, for first/last/deposit on a new place of residence. It is also a big gamble for those at the lowest end of the spectrum, where jobs are mostly "apply in person" and there's really no way of lining something up before making the leap. Plus there's the time without a paycheck - after the old job ends, if there is one, before the first payday at the new - and potentially waiting periods for being able to resume any public assistance the family is receiving if the move takes them across state lines.
We hope to relocate to another state in a few years, when the kids are off to college, and we figure we need at the bare minimum 3 months' living expenses plus $10k for moving and securing housing to pull it off. Not many people who are living paycheck to paycheck or unemployed in a depressed area can put that kind of money together. And that's not taking into account family ties - lower income families tend to be more inter-generationally reliant, in terms of grandparents or aunts/uncles helping with childcare, adult and teen kids/grandkids helping with elder care, etc. Detaching from that non-monetary safety net incurs costs as well.
And that's another discouraging facet. It takes a lot more to get your foot in the door than it used to, which handicaps college grads who had to work their way through and didn't have the luxury of lining up an impressive portfolio of unpaid internships with the "right" companies. I've been seeing this a lot with my classmates - the middle class kids who had parental help with college and a car that they didn't have to pay for are doing far better, 6 months after graduation, than the ones who were too busy working to take on multiple internships and on-campus activities, or who were relying on public transportation and couldn't get to the most desirable student jobs. It is easily the difference of $10-15K in starting salary, not to mention a much easier path to a job in a hard field to break into.