Few situations hold more promise for a theatrical evening than a chance encounter in a public place between two strangers. The opening steps are hesitant but lead to the discovery of common interests before a more profound relationship is forged, though not without intimations of heartbreak. The granddaddy of the genre is the David Lean film Brief Encounter (from Noël Coward’s Still Life), which is cloned by French playwright Yasmina Reza in The Unexpected Man, albeit with a clever twist.

The play, by the Tony-winning author of Art, had its English-language premiere in London in 1998; that was followed by a New York production starring Alan Bates and Eileen Atkins in 2000. The Man and the Woman, as its two characters are identified, spend almost 90 intermissionless minutes sharing a train compartment. The Man is a celebrated author but fears he has passed his prime and popularity. The Woman, a prodigious reader, is a fan who has the Man’s latest book, The Unexpected Man, in her pocketbook, having intended to read it on the train. Most of the text is composed of alternating monologues that are revelations of the characters’ personal demons. The two become increasingly aware of each other, she more than he, but they barely speak until the climactic exchange that brings them together.

The lights come down on an ending as fraught with possibilities as that of The Lady or the Tiger, but with a different kind of danger. The unspoken question does not seem to be whether the two will leave the train together but whether either can abandon a solitary life to let the other in. And if they do, whether happiness is an obtainable or even a desirable condition for two people of a certain age who are so wrapped in melancholy defenses. The tiny Wellfleet Harbor Actors Theater, set amid the fog and mists of Cape Cod, provides a milieu that makes it easy to believe in Reza’s premise regarding the isolation of one individual from another.

Under David Wheeler’s direction, the play unfolds simply, with two actors seated opposite each other in Dan Joy’s stylishly crisp art deco setting of two oversized banquette-type railroad seats. The chairs are patterned with swiftly moving light that, with Haddon Kime’s sound collage, suggests the ever-changing view out the windows of the Paris-Frankfurt train crossing Europe through the night.

Paul Benedict (think all those seasons on The Jeffersons, plus a host of other television shows and films) portrays the Man in properly introspective fashion, conveying an understanding of the pettiness of his problems even as they consume him. Benedict’s natural facial expression — it’s as if the gravity of the ages were waging a battle for the corners of his eyes and mouth — is a mirror of his character’s ennui and discontent. The first word out of his mouth is " bitter, " an adjective he uses to describe his discomfort at a friend’s dismissal of The Unexpected Man.

Lisa Richards is the aged ingenue who once was beautiful and adored but has sunk, both in posture and personality, into the passing years with a barely suppressed anger. She has lost too many people who once loved her, and even when present they were disappointments. She doesn’t know whether or when to pull out the volume, or whether the author will notice her reading it, and that leads to the obligatory climax, as Benedict — the actor as well as his character — ignites.

Wheeler’s casting and direction stress the idea that it is never too late to gather some rosebuds. Benedict and Richards make you long for a happy ending, however elusive that commodity is in real life.