In this hypothetical future where the United States no longer exists, the future "poor" people are likely to still be better off than poor people of today, even possibly middle class people of today.
That depends on some VERY specific circumstances being in place, not least of which is the successor of the U.S. government being at least as socially responsible as the current one. One can hardly guarantee this after an unexpected regime change; the imposition of, say, a Fundamentalist Mormon Theocracy would suck pretty hard for anyone who isn't a white male Mormon with working ties to the finance sector. Whole ethnic groups being forcibly relocated to ghettos probably wouldn't buy the "We're better off" theory just because you can cure breast cancer cancer with $23 prescription.
Just compare today's poor people to those of 100 years ago. If you had a time machine, went back to 1900,
100 years ago was 1912, the height of the gilded age. Comparatively, the poor AREN'T that much better off today. To begin with, there's a hell of a lot more OF them, and the unemployment rate is considerably higher at a time when average purchasing power for the lower two quintiles is actually LOWER than it was during the great depression. The Census Bureau intentionally changed the way they measure the inflation rate for this very reason: because people were getting pissed off at the rising cost of essential goods, so they rolled non-essential goods (computers, cell phones, TVs, etc) into the calculation to balance things off.
In what way are the poor better off than 100 years ago? Their legal and civil rights have far stronger protections, and the social structure of the country has been largely reformed. To assume this would still be the case after the disbandment of the Union would be to assume continued economic and social/political progress DESPITE institutional upheaval, and that's not even a safe assumption if the United States continues
to exist. It's just as possible that Jim Crow segregation will go back in style by the 2050s, this time divided up by economic class.