Joel and Ethan Coen's comedy-thriller Fargo was an instant smash upon its release in 1996, earning accolades and box office receipts unlike anything the brothers' earlier work had achieved. Its screenplay even won an Academy Award, in recognition of its tight plotting and strikingly unique tone. But one thing that has always puzzled audiences, even some of the film's most ardent fans, is the significance of a particular character who is only present for a single scene: Marge Gunderson's old friend, Mike Yanagita.
In the midst of her investigation into the film's central kidnapping, Marge (Frances McDormand) accepts a lunch invitation from her high school acquaintance, Mike (Steve Park). He awkwardly fumbles through their conversation, telling her about his marriage to their classmate Linda. Linda, he reveals emotionally, recently died of leukemia, leaving Mike desperately lonely. Later, Marge relays the uncomfortable encounter to another friend over the phone, and learns that not only is Linda alive, but she was never married to Mike and in fact had to get a restraining order to protect herself from his obsessive stalking. Marge is visibly disturbed, but never mentions the situation again.
As documented by Vox, there are two popular theories about the Coens' intentions in this scene, and both can be true. First, Mike Yanagita does have more impact on the main kidnapping plot than appears on the surface. One of the film's primary themes is the way the "Minnesota Nice" pleasantries of the Midwestern characters masks the shame and fear that can drive a man to desperation. Marge only approaches Jerry Lundegaard (William H. Macy) for a second interrogation after the Yanagita episode, and though she never says as much, it's because her unwavering trust in the honesty of those around her has just been challenged.
The other interpretation, as espoused by Noah Hawley, creator of the spinoff Fargo TV series, has more to do with the overall tone struck by the Coens. Fargo opens with a title card claiming that the film is based on a true story that occurred in 1987. It isn't, but the specificity of that date, combined with apparent non-sequiturs like Mike Yanagita, primes the audience to be more willing to explore the space of an absurd story. As Hawley explains, "It's one of those details where you're like, 'Well, they wouldn't put it in the movie unless it really happened.'"