If you look outside the US, you can get housing for a price that leaves enough of the 4000 for other expenses.
The easiest option is to connect some barren land to a city center with public transport in a climate zone that doesn't need much insulation. But that just as a proof of concept. More clever options can be realized.
People live off one dollar per day.
The most expensive part is medical insurance. That has to come down to international standards. 300 dollars a month should be enough.
You need food from a central kitchen, about 1 dollar per day.
That leaves 4000 dollars for rent, clothing, phone and other expenses.
I think you can work out the next flaw in the plan for yourself.
You call it flaw, I call it obstacle.
If you look outside the US, you can get housing for a price that leaves enough of the 4000 for other expenses.
The easiest option is to connect some barren land to a city center with public transport in a climate zone that doesn't need much insulation. But that just as a proof of concept. More clever options can be realized.