Even with low cost housing you have to be careful.
It's up to the owner of the property whether he/she leases or rents their property to them. They (meaning property owners) have you pay for a credit check. (in California). Most (meaning property owners) have high standards. Unless you find a slumlord.
Low cost housing and even Hud just regulates how much a property owner can rent their property for and or help to make property somewhat affordable by setting standards (how much a owner's property can rent/lease)for people that are low-income.