Then, on July 7, almost a year to the day after the couple first showed up at the homeless intake center, Ms. McGuire wrote online, “Looks like things are finally looking up,” adding the hashtags #lifeisgood and #onedayatatime. She had gotten a state license to work as a security guard, she wrote, and Mr. Ambrose had worked his first job as a house painter.

Everything would change on Dec. 7. It was a “freak accident,” according to Mayor Bill de Blasio: A valve had come off a radiator in the room where the girls slept, filling the room with intense heat and steam. It was not clear how long the steam had been pouring out, or whether the girls’ cries had gone undetected. A neighbor, hearing the parents’ screams, called 911 at 12:08 p.m.

Fifteen minutes later, the girls were declared dead.

It was a horrific story that focused attention on the bizarre cause, the tragic outcome and the somewhat unusual route the family took to establish a home in Hunts Point, where the city maintained a so-called cluster site: several apartments reserved for the homeless in a private building. Apartments like the one the Ambrose family stayed in are meant to be a temporary form of shelter, but the family stayed there more than 13 months.

Growing Up in Poverty

Houlton, a town of about 6,000 residents, is the seat of Aroostook County, known as the Crown of Maine, but it is one of the poorest in the state, where one in six people live in poverty. The county has the state’s lowest median household income, just $36,066, slightly higher than the Bronx, although with a more affordable cost of living.

Crystal meth and opioid use, as in so many small towns, was rampant. Through the end of September, 12 people had died this year from drug overdoses in Aroostook County; statewide 286 people had died from overdoses through that date, already surpassing the 272 overdose deaths in all of 2015, according to the Maine attorney general’s office.