The weekend before John Patrick Shanley’s latest play, “Brooklyn Laundry,” opened, I was supposed to see the Saturday matinee. A non-Covid illness forced its cancellation, though, and required understudies to perform that evening and the next day, as multiple company numbers were affected, according to a publicist.

The development was unfortunate, but not entirely inappropriate: Health problems play a substantial role in “Laundry,” and in general a lot of bad things happen to the characters. In the first scene, the owner of a laundromat explains to a customer how he got an unexpected financial boost after being struck by a car, thanks to a legal settlement.

The client, a beleaguered woman played by a “Saturday Night Live” alumna, Cecily Strong, responds, “Why doesn’t anything like that happen to me?” As it happens, before this one-act, 80-minute piece has run its course, she too will be hit — figuratively, but profoundly, and more than once.

Ms. Strong’s character, Fran, already has amassed a history of suffering by the time we meet her. Approaching middle age, she’s stuck in a job she loathes, and hasn’t had much better luck with men. Her two sisters, who will appear later in the play, have married and had children, but their own struggles and even worse fortunes are quickly revealed. 

As for that laundromat owner, Owen — played here by the reliable David Zayas, with his usual scruffy, low-key charm — Mr. Shanley, who also directs this production, doesn’t suggest he’s had it easy, but the character is clearly more inclined to count his blessings. Early on, Fran, who will become his love interest, asks him if he believes in God, and he points to his own progress as a basis for faith.

Fran, predictably, is more skeptical. Owen pegs her as “gloomy,” likening her to an ex-girlfriend; rattled by this observation, she shows up for their first date high on mushrooms, and gets Owen to partake as well. A lovely, funny scene follows, beautifully played by Ms. Strong and Mr. Zayas, in which the fledgling partners reflect on the little examples of wonder surrounding them, including each other. 

Owen also, perhaps under the drug’s influence, tells Fran of personal obstacles and fears; she is less forthcoming, a factor that will threaten to undo the relationship. Mr. Shanley, who has won an Academy Award, a Tony Award, and a Pulitzer Prize for his surveys of the particular challenges facing women — the first for the 1987 film “Moonstruck,” the latter two for “Doubt,” presently being revived on Broadway — justifies this, in a sense, by establishing a sharp and somewhat quaint contrast between the male and female characters informing “Laundry.”

While Owen is the only man who turns up onstage, we learn quite a bit about Fran’s sisters’ husbands — one of them estranged — and a little about their late father, and suffice it to say that none of it is encouraging. The sisters, played by Florencia Lozano and Andrew Syglowski, both excellent, end up burdening Fran in part because neither of their men is man enough.

We’re led to worry, at one point, that Owen will prove similarly disappointing, but “Laundry” wraps with an unabashedly romantic twist that, without dispelling those doubts altogether, leaves us cautiously optimistic. 

One other guy we don’t see deserves praise: the veteran scenic and costume designer Santo Loquasto, himself a four-time Tony winner, who for this production has crafted a revolving set that takes us to several vividly represented locations, from the laundromat to an outdoor café at Brooklyn to a trailer home in rural Pennsylvania.  

If “Laundry” isn’t likely to score Mr. Shanley another Pulitzer, its unfussy, old-school lyricism feels like good medicine right now — for the spirit, at least.