Oh no, I totally agree. The middle class is a rapidly shrinking population. I don't really know anyone in my life who is middle class. We are all relatively poor, and our parents are either right along with us, or upper-middle to upper class.
I don't know if the term is officially called dual coverage. It just means that you are on medicaid and medicare. If you are on medicaid, and are also on SSI or SSDI, you will receive an invite to join medicare after about a year. It's really not an invite, actually. You are required to join. It's like one of those record of the month letters... if you do nothing, you will be enrolled. You get parts A and B. Now, of course, you also get part D, which is the drug coverage.
A lot of people who are on federal disability have dual coverage like this. It's really the best way to go if you're poor and disabled, because medicaid serves as a supplementary insurance, so whatever medicare doesn't cover in terms of doctor's costs, medicaid will. Although I'm sure it varies from state to state.