It is estimated that about 1% of the total housing stock in New York City is rent controlled (2019 figure), which is something different than rent stabilized.

Generally the way the former works is that you have to have been living continuously in the home since July 1, 1971, and the building itself needs to have been constructed before 1947. If this is the case, then in theory, you should have seen relatively minor rent increases over the years.

This was the case for the late real estate agent, Alice Mason, who died at the beginning of this year at the age of 100:

She never left the rent-stabilized [controlled?] apartment where she held her storied dinners, in a century-old building on East 72nd Street. (In Manhattan real estate parlance, it was a classic eight, a gracious prewar layout that included three bedrooms and two maid’s rooms.) In 2011, the developer Harry Macklowe bought the building for a reported $70 million and began to turn the units into condos, buying out the tenants to do so. But Ms. Mason refused to give up her apartment. When she moved there in 1962, the rent was $400 a month. At her death, it was $2,476. The apartment below her, in the same line, was recently on the market for just under $10 million.

Green, Penelope. “Alice Mason, Real Estate Fixer and Hostess to the Elite, Dies at 100.” The New York Times, 13 Jan. 2024, www.nytimes.com/2024/01/11/style/alice-mason-dead.html.

For better or for worse, this is an obviously awesome deal, and reason enough to never move and have family members move in with you before you die so that you can try and pass down this asset for generations to come.