For $90 a night, it was one of the cheapest Airbnbs in Chelsea, an affluent neighborhood bustling with art galleries and night life in the heart of Manhattan.

But when Rachel Valerio and her mother retrieved the apartment keys from a lockbox outside and opened the door to the seventh-floor apartment, something seemed off. Despite the listing’s near-five star rating on Airbnb, it smelled like gas, and Ms. Valerio was alarmed by the roach trap next to the bed.

“Then I saw the letters N-Y-C-H-A in the lobby,” said Ms. Valerio, who was visiting from Boston.

After a quick Google search, she learned it was the acronym for the New York City Housing Authority, the nation’s largest public housing system, which houses 400,000 low-income residents.

They had checked into a public housing apartment.

The listing was an unlikely entangling of two of the most publicly debated housing issues in New York City: the future of the city’s 176,000 crumbling public housing apartments and the proliferation of Airbnb, which has 50,000 listings in the city.