Opinion | One Year Inside a Radical New Approach to America’s Overdose Crisis

He had not thought much about why that was. His life had been rough, by almost any metric. He saw his first killing, in a barrio in San Juan, P.R., when he was 4 years old; he still remembered touching the brains that had spilled across the sidewalk and being yelled at by some adult to get inside. He remembered other things, too, some of them done to him, that he preferred not to discuss. He’d fallen into drugs early and suffered the usual consequences and then some. In 2010, just a few days after he’d gotten out of prison (two years that time, for attempted robbery), his daughters and their mother were stabbed to death.

Still, he did not consider himself a depressed person. And if he eschewed human connection, he was not entirely without ambition. He’d love to have a job — maybe to be a cook again if he could — and his own place one day, if possible. But he spent most of his waking hours in pursuit of something else, a feeling that he could not quite describe. Maybe the closest word to it was “peace.”

Drugs sometimes got him there. Talking about sad things did not, but Mr. Cosme liked Ms. Corso instantly, and in the weeks that followed his overdose, he found himself telling her all sorts of things he had never told anyone. He did not think of it as therapy, whatever that was. They were just talking. She had offered to help get him on buprenorphine, a medication that eases opioid cravings, so he could stop taking heroin, and he was considering it. She was also talking to him about jobs he might want to do one day and places he could live.

It could take a month or more to get someone like Mr. Cosme into a supportive housing or inpatient program. “The amount of paperwork we have to submit and the level of proof we have to provide for every single need is prohibitive,” Ms. Corso said. “It can be a full-time job just getting one person placed, and we are never dealing with just one person.” Paperwork was not the only barrier. People who were ready to enter treatment were often turned away because they stopped using a few days earlier and were therefore deemed not to be in crisis. Mr. Webb had shepherded one actively suicidal man to the hospital, only to be told — almost casually — to take him to detox instead.

The policies and rationalizations undergirding such decisions were infuriating and nonsensical. But the real problem, as everyone knew, was a shortage of available programs. Project Renewal Support and Connection Center, a short-term care facility on East 116 Street, was the team’s favorite option, by far: beautiful facilities, amazing staff. But it had only around 16 beds (13 for men, three for women), and it could keep people only for five or so days.