The landlord in public housing is a public housing agency, a body created under state law rather than an arm of HUD. HUD's role is to fund and regulate. Section 1437g of Title 42 establishes the Capital Fund, which pays for development, modernization and major repairs, and the Operating Fund, which covers the gap between the rents residents pay and the cost of running the properties. Because tenant rents are set as a share of tenant income rather than by the market, that operating subsidy is not a supplement to the business model; it is the business model.
Rent is where the most confusion sits, because two different rules apply and the widely repeated "30 percent of income" is neither of them exactly. The general rule at 42 U.S.C. 1437a(a)(1) is a highest-of test. A family pays the highest of 30 percent of monthly adjusted income, 10 percent of monthly income, or the designated housing portion of a welfare assistance payment. Note the parenthetical in that sentence, which excludes families assisted under section 1437f(o) or (y), the voucher programs. That exclusion is about which provision governs rather than about substance: 1437f(o)(2)(A) writes the same greatest-of test into the voucher program directly, so a voucher household's own share is computed the same way. Layered on top, 1437a(a)(2) gives public housing families something voucher holders do not have. Each family must be allowed to elect annually between an income-based rent and a flat rent the agency establishes for the unit, and the agency must offer both. The income-based figure is a ceiling rather than a fixed amount: 1437a(a)(2)(B)(ii)(I) provides that it may not exceed the greatest of the three amounts in the highest-of test, and adds that the clause "may not be construed to require a public housing agency to charge a monthly rent in the maximum amount permitted". Most agencies charge the maximum, but the statute does not make them. A separate provision at 1437a(a)(3) lets an agency impose a minimum monthly rent of not more than $50, and requires an immediate hardship exemption where a family cannot pay it because it has lost or is awaiting a benefit determination, would be evicted, has lost income, or has had a death in the family.
Who gets in is governed by two layers. Income limits come from 1437a(b)(2): low-income families are those at or below 80 percent of area median income, very low-income at or below 50 percent, and extremely low-income at or below the greater of the poverty guideline for the household size or 30 percent of area median income. On top of that sits an income-targeting requirement at 42 U.S.C. 1437n(a)(2): of the public housing units a housing agency makes available for occupancy in a fiscal year, "not less than 40 percent shall be occupied by extremely low-income families". The parallel rule for new voucher assistance at 1437n(b)(1) is 75 percent, so the two programs target the deepest poverty at different intensities.
Waiting lists are ordered rather than first-come. Under 24 C.F.R. 960.206 a housing agency may adopt local preferences based on local housing needs, may limit the number of applicants who qualify for any preference, and must tell applicants what preferences exist. Residency requirements are prohibited, though a residency preference is not. The honest description of access is therefore that lists are frequently closed and, when open, preference-ordered. There is no defensible national figure for how long a wait takes, because the answer is a property of the individual agency's list and its preference system.
The supply side explains why those lists behave as they do. Section 1437g(g)(3), under the caption "Limitation on new construction", bars a housing agency from using Capital Fund or Operating Fund money to construct a public housing unit if the construction "would result in a net increase from the number of public housing units owned, assisted, or operated by the public housing agency on October 1, 1999", counting units demolished in a revitalization effort. This is universally called the Faircloth Amendment, a nickname that appears nowhere in the statute. Two exceptions follow, and neither is a general escape hatch. Subparagraph (B) lets an agency spend Capital or Operating Fund money on units above the cap while denying it any extra formula funding for that purpose, and subparagraph (C) lets the formulas cover the operating and modernization costs, though not the initial development costs, of excess units that are part of a mixed-finance project or otherwise "leverage significant additional private or public investment". Meanwhile units leave. HUD's Rental Assistance Demonstration, announced in 2012, "provides the opportunity to test the conversion of public housing and other HUD-assisted properties to long-term, project-based Section 8 rental assistance". A converted property is no longer public housing under the 1437a(b)(1) definition, because its assistance now comes under section 1437f. The stock is capped at one end and draining at the other.