There are certain programs in NYC like CityFHEPs and HUD housing throughout the US for people in a homeless shelter on cash assistance and/or some other conditions, making it possible, but quite difficult, for the average person to get a housing voucher (that allows the client to pay only 1/3rd of his or her income).
I was just going through the economics in my head as well as going through the breakdown of the annual US budget, and was trying to calculate how many tax payer dollars would it actually cost for the US government to give similar vouchers (paying most of the rent if an apartment/mini house or room up to $2400 allowing the client to pay one third of his or her income), to all Americans making within 40k per year, let's say.
How much would such an operation cost annually? We would need statistics on how many Americans make less than 40k per year.