PARK CITY, Utah — It’s quite a tale: Seven children, all with waist-length hair, are raised on welfare in a messy four-bedroom apartment on the Lower East Side of Manhattan. And they are almost never allowed to leave the house. For years.

Their father has the only key to the front door, and he keeps it locked. In some years, they are allowed outside only a handful of times. In others, not at all.

The kicker is that the story is true — and all but one of the children still live there.

“The Wolfpack,” making its premiere at the Sundance Film Festival here on Sunday, is one of those truth-is-stranger-than-fiction documentaries that come along on the rare occasion a filmmaker happens to be in exactly the right place at exactly the right moment. In 2010, Crystal Moselle, the film’s director, bumped into six of the Angulo siblings — boys, then aged about 11 to 18 — on one of their rare trips outside and befriended them.

Eventually, they allowed her to bring a camera inside the apartment. “I was their first friend, and I think they were as fascinated by me as I was by them,” Ms. Moselle said. “Slowly their mom warmed up. The dad was definitely a roller coaster.”