The
421a tax abatement program allows developers to build condos or co-op buildings with an exemption from property taxes over a certain number of years. The period of tax abatement depends on the location of the building. Some areas are excluded entirely from the program unless they meet certain requirements (such as setting aside 20% affordable housing).
Certain areas of the city fall under the rent-stabilization guidelines (which is governed by the Department of Housing and Community Renewal; NYCHA has nothing to do with rent controlled or rent stabilized apartments, but rather government-owned public housing). The entire borough of Brooklyn, for example, is theoretically entirely rent stabilized unless the landlords can prove they provided enough capital improvements to an apartment unit to justify making it a free market unit. Of course, rent stabilized in this case means a rent of $2,500 a month or less, and this is still above market rates for much of Brooklyn.
In other parts of the city, certain units are either rent controlled or rent stabilized for whatever given reason. In the case of free market apartments, the landlord holds all of the cards against the tenant because the leases last only one year. If the landlord wants you gone, he simply won't renew your lease. For RC/RS apartments, the opposite is true. My boss recently offered $800,000 to buy out each of the four RS tenants living in a building he wanted to sell around Washington Park, and they all said no. So they stayed, and the new owner bought the building even with the condition that those RS tenants would continue to live there, and can never be kicked out according to the law.
For buildings built under the 421a program, if they can't be sold as condos or co-ops for whatever reason (weak market, etc.), they can be converted into rentals. The caveat is that these rentals will remain as rent stabilized over the entire tax abatement period.