Margot Miller, who has been living at a convent in Harlem, was disqualified from an apartment because she had once been sued by a landlord, landing her on a tenant blacklist.CreditMichelle V. Agins/The New York Times

After two years of being homeless, napping in stores open all night and more recently staying in a convent in Harlem, Margot Miller found out in March that her luck was about to change: She had qualified for an apartment for low-income older adults.

“This is to inform you that a rental unit has become available,” the letter from the building’s owner, Prince Hall Plaza, began.

Elated, Ms. Miller, 68, said she immediately went to the building’s office to claim the apartment. But after a background check, she said, the building reversed course.

“I go there, I’m all excited,” Ms. Miller said. “The woman there then does something on the computer. Then she said, ‘You can’t have this.’”

She was disqualified, the woman told her. Not because of her credit score. (At 760, hers was stellar.) And not because of a criminal record. (She had none.)