It has been nearly a quarter-century since Roy Fox had a regular salary. He is not a lottery winner or the recipient of some grand family fortune. He is, in short, the type of person who long ago would have been priced out by New York’s ever-climbing housing market.

But for more than two decades, Mr. Fox, a retired radio host who earns a modest pension, has been enviably situated in an airy abode with park views, burnished wood floors and historic detailing. In fact, he is the sole resident of a 29-room mansion in Jamaica, Queens, constructed before the Declaration of Independence was written — a pre-prewar, so to speak.

If paying scandalously low rent for one of the city’s 39,000 remaining rent-controlled apartments is viewed as the holy grail of New York real estate, that is only because so few are aware of the existence of an even more elusive and lustrous prize.

Mr. Fox, 72, is one of only 19 people lucky enough to seize the role of resident caretaker of a city-owned historic home, a job that comes with no salary but a perk so seemingly lavish that many are loath to admit it to their friends: they not only live in some of the city’s most splendid manors, but they also do so completely rent-free.