‘Affordable housing’ is an overloaded term at this point. There are people who qualify for ‘affordable housing’ in NYC who are making ~$180,000 and will be paying $3,000/mo or more in rent after their ‘low-income subsidy’ is factored in.
It does appear to be the case that you can qualify for "affordable housing" in NYC if you make $180,000/year ... and have a family size of at least 3. (In fact, it goes up to $290,565/year with a family size of at least 8.) However, the category of income this represents is "middle income", one level above "moderate income" and two levels above "low income". Even with a family size of 8, "low income" caps out at $140,880/year. It appears that approximately half of new affordable housing targets "low income", and most of the remaining half for incomes lower still.
(The specific term "low-income subsidy" appears to mostly refer to the "Medicare Part D Extra Help Program" and cuts off below $35k/year.)