I can't see anything obviously wrong in that reasoning, but in Italy that situation has more-or-less obtained for decades and I can't see any sign of such a process happening.
I guess what's happening is some process preventing the standards of some members to fall much below the standards of the rest of the society. (If you know your children will be ostracized by their peers, making their life much harder, unless they wear expensive clothes, have expensive toys, etc., then you might not want your children to wear cheap clothes and have cheap toys, even if in isolation they'd enjoy them just as much as expensive ones.)
It'd be interesting to know what is going on. If you argue from a sort of Malthusian ideological-lowering-of-subsistence-wages, that doesn't explain it since the subsistence wage is still way below the regular wage and ought to allow indefinite over-reproduction of the subpopulation. And these subpopulations often isolate themselves from the world and denigrate it as much as possible, so the world's standards shouldn't matter too much to them.
My own suspicion is that there's some sort of diseconomy of scale to these subpopulations: they grow like gangbuste...
I was browsing my RSS feed, as one does, and came across a New York Times article, "A Village With the Numbers, Not the Image, of the Poorest Place", about the Satmar Hasidic Jews of Kiryas Joel (NY).
Their interest lies in their extraordinarily high birthrate & population growth, and their poverty - which are connected. From the article:
From Wikipedia:
Robin Hanson has argued that uploaded/emulated minds will establish a new Malthusian/Darwinian equilibrium in "IF UPLOADS COME FIRST: The crack of a future dawn" - an equilibrium in comparison to which our own economy will look like a delusive dreamtime of impossibly unfit and libertine behavior. The demographic transition will not last forever. But despite our own distaste for countless lives living at near-subsistence rather than our own extreme per-capita wealth (see the Repugnant Conclusion), those many lives will be happy ones (even amidst disaster).
So. Are the inhabitants of Kiryas Joel unhappy?