For the first time in 15 years, thousands of people who cannot afford to live in New York City may be able to get financial help through a highly sought-after federal program.

Then they will face another obstacle: the city’s scarcity of apartments.

The New York City Housing Authority on Monday reopened a waiting list for housing choice vouchers, a federally funded program also known as Section 8. The list closed in December 2009, after it ballooned to include more than 128,000 families seeking help.

Now, that waiting list has dropped to 3,700 households, prompting NYCHA to reopen it.

Vouchers help more than five million people nationwide, but in no place is the program as expansive — and perhaps as needed — as in New York City. Here, nearly a quarter of a million lower-income New Yorkers rent apartments on the private market using vouchers. Under the program, people spend at most 30 percent of their income on rent while the rest is paid for by the government.

The vouchers can be a lifeline for lower-income families, but it has become harder to find apartments where they can be used.

In 2018, more than 70 percent of families with children were able to find an apartment to rent with their voucher within a year, according to an analysis by the New York University Furman Center. In 2022, that number had dropped to 58 percent.

That reflects both the extreme housing shortage and a continued reluctance on the part of landlords to rent to people with vouchers, according to the Furman Center analysis. A city survey showed that the rental vacancy rate was 1.4 percent in 2023, the lowest in more than 50 years. The rate was even lower for cheaper apartments.