What had happened in between?

There are roughly 3,900 unsheltered homeless people in New York City, ever visible but also largely anonymous. They lie in dingy sleeping bags near buildings or construction sites, bury themselves under blankets, ponchos and cardboard boxes, or sit with propped-up signs asking for money. Their presence remains one of the most intractable challenges facing the city: Solutions are complex at best, and finding the proper balance of medical care, casework and law enforcement to ease them off the streets has proved daunting to the de Blasio administration, as it has been to many that came before.

Over the course of more than a year, I delved into Nakesha’s life, trying to understand the events and forces that put her and so many of the city’s homeless on the street. I spoke with dozens of people and benefited from having access to hundreds of emails that Nakesha sent over the years to friends and others, and scores of meticulously typed letters that she copied at libraries and handed to passers-by. In these, she offered a winding, rudimentary diary of her existence on the street.

My effort revealed a deeply complicated, at times contradictory, journey — a life of spectacular promise undone by demons. No simple answer to the puzzle of Nakesha emerged. But at the same time, another narrative revealed itself: a story of New Yorkers and others who went to extraordinary lengths to try to help her, only to be left frustrated.

On her grate at East 46th Street and Park Avenue, Nakesha was surrounded by a collection of strangers who offered their company, care and generosity. Sidewalk vendors watched over her and her belongings. Restaurant owners let her use their restrooms. People like P.J. brought her food and warm clothing.

And yet Nakesha continued to spiral downward. She rejected P.J.’s suggestion that she enter a shelter or seek help. “I was like, ‘I have a friend that you can talk to,’” P.J. recalled telling her, referring to a social worker she knew. “She’s like, ‘Oh, no, I’m fine.’” P.J. tried again. “‘Do you need any medication?’” The answer was no.

So P.J. tried to address her other needs. She brought her sandwiches and toiletries. She went online and ordered her a raincoat, a duffel bag, two pairs of black pants, shirts, socks and underwear. She bought a pair of black leather boots that she helped Nakesha pull over her swollen feet. She gave her presents on her birthday and at Christmas.