A pair of Eleanor Rigbys — lonely people stuck in a remote town in way-upstate New York — meet every morning over a diner counter. She’s a 30ish woman (Susannah Flood) who’s fled a failed situationship seven hours away and distracts herself with the routine of filling coffee mugs and working for tips. He’s a 60ish retiree (Anthony Edwards) who tromps into the diner in a heavy winter coat just as the diner opens each morning as a distraction from a life that feels thwarted both professionally and personally. If you think this is some kind of intergenerational meet-cute, think again. While romantic fulfillment is something that preoccupies both Katie and Paul, Meghan Kennedy has other plans for her characters in the deliberately low-key drama The Counter, which opened Wednesday at Roundabout’s Laura Pels Theatre Off Broadway.

Early on, Edwards’s Paul enters an implausible pact with Flood’s Katie that amounts to an ongoing mutual therapy session, with strings attached. You see, Paul really wants to off himself after a life in which he set aside his own ambitions and desires to take on familial responsibilities. He dropped out of the Peace Corps to return home and care for his ailing mother, then looked after his more outwardly successful brother, who squandered his fortune on pricey nursing care. The timing of Paul’s final exit he leaves to Katie, who as a near-stranger seems like the least likely person to follow through on his wishes. But she outwardly goes along with the plan, and leans on her conversations with Paul to break her own two-year pattern of avoidance about how she blew it with her ex not-quite boyfriend. With Paul’s help, she even starts to play the 27 voicemails that the guy left on her phone that she hasn’t had the will to delete.

None of this makes much sense, to be honest, but Flood and Edwards radiate a realness and earnest vulnerability that overcomes the improbabilities of the premise. Under David Cromer’s typically unfussy direction, this slender, one-act play has a fablelike quality that’s belied by the hyper-realism of Walt Spangler’s set design and costumes (by Sarah Laux) that look like they could be worn in a 21st-century version of an Edward Hopper painting. We never see any other employees at the diner, or any other customers for that matter — aside from a brief appearance by the local doctor (Amy Warren) who seems to be the only other person in town who knows both Katie and Paul. She also fills in some of the backstories that these stubbornly independent souls are unwilling to share with each other.

It’s a wonder that these two open up at all. Perhaps as a result, Kennedy leans heavily on deus ex machina devices, shifting key incidents offstage so that we’re left to wonder how the characters actually reacted in the moment. Perhaps that’s just as well. The Counter offers a portrait of two individuals whose self-isolation has curdled into a kind of solipsism, one that shuns any intrusions from others. But when an intrusion does come along, the play seems to suggest, it’s best to be alert to the possibility of change. And to welcome it in, with a pot of fresh brew at the ready.

THE COUNTER
Roundabout’s Laura Pels Theatre, Off Broadway
Running time: 75 minutes (no intermission)
Ticket on sale through Nov. 17