New York City homeless shelters—swelling with record-high populations not seen since the Great Depression—are increasingly being sought out by people who participated in a now-defunct rent-subsidy program designed to reduce homelessness, according to a report to be released Saturday.

The author of the report, the Coalition for the Homeless, a nonprofit advocacy group, held up the report as evidence that homeless families need longer-term government help with rent to stay out of the shelter system. Since the rental-payment...