Hit & Miss, which ran on British television earlier this year to an enthusiastic reception, was created by Paul Abbott, whose own rough-and-tumble childhood — he was one of nine children who raised themselves in public housing after being deserted by both parents — has given him an enduring fascination with the hidden strengths and heartbreaking vulnerabilities of children left on their own. (He’s also the producer of Shameless, Showtime’s scabrous underclass comedy-drama.)

In Hit & Miss, he blends that with the unique workplace conundrums imposed on Mia by her new motherhood. Slitting a man’s throat and leaving him on the couch to be discovered by his wife and children for the first time loom for her as moral questions rather than logistical bumps in the road.

It’s not an entirely successful formula. Sevigny is at her weakest in the brawling gangster scenes, where her unimposing physicality is not at all convincing. (And hasn’t anybody in Great Britain even seen The Godfather? Mia is the only hit man — er, person — in the history of gangster guignol who doesn’t shoot her targets in the head.)

But she more than makes up for it in the scenes where she has let down her defenses to try to persuade the reluctant kids to drop theirs. Hurt, hesitant and humbled, she’s a poignant portrait of a woman who has been dealt a bad hand by life and is playing it as best she can. About all she can hope for is hope. When Ryan, terrified at the way the family’s life is spinning out of control, tells her that he doesn’t want things to change, Mia gently replies, “Without change, there wouldn’t be any butterflies.” Listen closely while watching Hit & Miss and you may hear the gentle swish of tiny wings.