McCollum is a community health worker, hired to help patients stay healthy - and, crucially, out of the hospital - in the weeks after they are discharged back to the community. Some need a primary-care doctor. Or a way to get medications delivered. Others need their electricity turned back on.
McCollum asked Tiller what he needed help with.
"Recovery," he said, after 43 years addicted to alcohol. "And getting back together with my family."
Community health workers - trained laypeople who share backgrounds with the people they help - are not a new concept. They have been an important part of health care around the world for decades, and are used in pockets across the United States. Usually they help with specific conditions, such as working with hypertensive patients to improve their diets.
Despite evidence that they improve outcomes, these workers have not found a place in mainstream care, perhaps in part because no one proved that they actually save the system money.
A new paper, based on what McCollum and another community health worker did at the University of Pennsylvania Health System, provides the first hints that they can.
For the study, in JAMA Internal Medicine, 446 adult inpatients from five high-poverty zip codes were randomly assigned to two groups. Patients in one were visited in the hospital by a community health worker, who helped with anything they needed for at least two weeks after discharge. The other group got usual care. Various measures, from medication adherence to mental health status, were taken after 30 days.
The assisted group turned out to be 50 percent more likely to follow up with a primary-care provider. And while there was no difference in hospital readmissions overall, those who returned to the hospital were far less likely to do so more than once if they were in the assisted group.
The results don't sound particularly dramatic. But the intervention lasted just two weeks.
"It was amazing how quickly [it] was showing results," said Garry Scheib, the Penn health system's chief operating officer. He tripled the size of the program, which is set to expand again, to 24 community health workers and a $1.5 million budget, by January.
Among the far-reaching parts of the Affordable Care Act are penalties that Medicare now charges hospitals for readmissions due to certain conditions within 30 days of discharge. The penalties - a relatively small $196,061 in the most recent year for the large Penn health system - have forced them to pay more attention to their patients' health after they go home. Poor patients are especially likely to be readmitted.
"Usually when we talk about risk, we talk about individual risk factors for specific diseases: Mr. Jones is a smoker, he is at risk for stroke," said Shreya Kangovi, a Penn assistant professor of medicine who led the new study. "But zip code is a risk factor for socioeconomic status - and that is a risk factor for everything."
Four years ago, as a pediatrician and internist in clinical practice, Kangovi and colleagues began systematically interviewing low-income patients in the hospital about what they needed to stay healthy and who could help them succeed.
"They wanted help with the kinds of things that were making them sick: food insecurity, trauma, the daily challenges that come with life in a lower-income population," Kangovi said. "Traditional health-care people, people like me, they can give you advice but they don't know what it's like in the real world."
Normally, doctors and nurses tell patients what they need. This program would be driven by patients. A key trait for community health workers, Kangovi said, is the ability to listen without judging.
"Let's say Mrs. Jones is 62 years old and isolated," she said, changing the name of a patient from the study. She has been admitted multiple times for panic attacks and chest pain.
"This time she meets Sharon," the community health worker, Kangovi said. "She looks like Sharon. Sharon asks her: 'What do you think is going on?' They talk for hours. They go home [together]. Maybe it's then that she says, 'I feel anxious.' "
Sharon: " 'What do you think you need to do?' "
Mrs. Jones: " 'I need to get out of the house more.' " She's afraid. So Sharon walks with her to the community center.
"All of a sudden," Kangovi said, Mrs. Jones "is getting a real intervention that is addressing the real cause of her condition."
At the Puentes de Salud health center in South Philadelphia, medical director Matthew O'Brien uses community health workers in more traditional ways: teaching classes to the largely Latino immigrant population, and working with patients on, for example, how to control or prevent diabetes. They do it very differently from how doctors and nurse practitioners would.
"I think social support is a key or the key element to success of the program," O'Brien said. "We have had patients who said this program has changed their lives."
Mary White, one of the two community health workers in the Penn study, had resources and connections in Southwest Philadelphia from years investigating child abuse and neglect in the neighborhood for the city. Penn gave her more training in medical and related issues for the $14-an-hour job.
When she started working with patients who were being discharged from the hospital, she discovered the reasons behind their admissions.
"People were coming to the hospital for things like elevated sugars. But they didn't have a glucometer" - essential for a diabetic to monitor blood sugar at home - "or they had to be shown several times over again until they got it," White said.
Sharon McCollum continues working with Al Tiller, the homeless man who is losing fingers to frostbite and was not part of the new study, to mend ties with his family. She located his daughter. But family visits at the Penn Center for Rehabilitation and Care can get testy.
"I keep the peace," McCollum said. "Or I will call her and say, 'Did you call your dad today?' "
Kangovi, who directs the year-old Penn Center for Community Health Workers, has meticulously tracked all their work. Posted on the center's website are six manuals and a free training course for other health systems that want to use the model. Several have expressed interest, and she's running a new study in which community health workers meet patients in primary-care providers' offices instead of the hospital.
Harrison J. Alter, an assistant clinical professor at the University of California, San Francisco, who oversees a community health program in his hospital's emergency department, wrote a commentary that accompanied Kangovi's article.
"This report is among the best evidence so far in support of what some are now calling upstream medicine, a term based on a common parable about children rushing down a river toward a waterfall," he wrote. "Rather than exhaust all resources to snag children as they pass, it seems only reasonable to send a party upstream to see who is throwing them in the river in the first place."