People have mentioned public housing, but it's probably more like renting out an apartment that has rent control (where there's a limit on how much the rent is allowed to increase each year). "Public housing" in the US has a connotation of being blocks of apartments/flats that are all managed by a government entity, where rent controlled units may be almost anywhere.

Could also be like Section 8 housing where I believe the landlord gets part of the rent from the government and part from the tenant (disclaimer: never lived in any of these, I could be wrong on details)