Performances don’t come more deadpan than the one Henry Rollins gives in “He Never Died,” an enjoyably strange horror film directed by Jason Krawczyk. Though perhaps “deadpan” is a poor choice of words, given that Mr. Rollins’s character, Jack, seems unable to die.

Jack has spent what turns out to be a very long lifetime perfecting the art of being nondescript, presumably to avoid getting into situations that lead him to indulge his taste for human flesh. For entertainment, he plays bingo. He goes to the same diner most every day. The waitress there, Cara (Kate Greenhouse, playing it perfectly), seems to be sweet on him, but somehow Jack, in his hundreds of years on the planet, has not mastered basic social skills, like holding a conversation.

But when Jack’s blood supplier runs into trouble with gangsters, his bubble of anonymity is breached, and his comfort zone is further intruded upon when he learns that he has a daughter (Jordan Todosey). The humor in Mr. Krawczyk’s script is deliciously subtle, as it has to be when your lead character is a man of few words; a viewer might easily spend the first half of the movie not even realizing it’s there.

The winking becomes more pronounced as the film goes along. Here’s Cara, trying to make small talk with Jack once it dawns on her that he’s centuries old: “So, the Civil War — what was that like?” But Mr. Krawczyk never lapses into over-the-top horror parody, which too many others have done too often.