I fail to see by what mechanism what you describes occurs. Do you constantly query your occupant of pay raises? Why would every raise be siphoned by rent? Poor people have problem making ends meet for clothes, food, etc. Sure, more money put inflationary pressure, but it's not a magic direct correlation and instant feedback. If the government is serious and declares that it will adjust basic income to match the market price for basic goods and regulate their prices, including building low-rent lodging, then the inflationary pressure will have to subsides into only unregulated items.