In a new revival of Sam Shepard’s “Curse of the Starving Class,” one cast member gets to provide comic relief and become a tragic figure without uttering a single word. Her name is Lois, and she’s a 4-year-old California Red sheep — last seen on the New York stage, her bio informs us, as a “featured actress” in the live Nativity scene included in Radio City Music Hall’s “Christmas Spectacular.”   

Although Lois is fully grown, her character evokes clichés attached to younger members of her species: sacrificial lamb, lamb to the slaughter. Of course, the sheep is hardly the only mammal who proves luckless in the play, one of several eviscerating classics in which Shepard explored family dysfunction on the fringes of the working class.

First produced in 1977, three years before Ronald Reagan was elected president, “Curse” has only gained power as an indictment of late-stage capitalism. Set in the rural West, where Shepard consistently found inspiration, the play introduces us to the Tate family. The patriarch, Weston, played here by Christian Slater, is an alcoholic prone to fits of violence; his wife, Ella, portrayed by Calista Flockhart, dreams of selling the farmland they own and moving to Europe.

It turns out that Weston, whose booze-fueled destructiveness has also led him to make foolish investments and accumulate debts, has his own clandestine plans for offloading the land. Ella’s romantic notions, meanwhile, have gotten her involved — in more than just a business sense, it seems — with another man, Taylor, whom she refers to as her lawyer, though real estate speculation seems to be his principal pursuit.

Weston and Ella’s precocious, rebellious daughter, Emma, played by a winningly wry Stella Marcus, is immediately suspicious of Taylor when he stops by, not long after Weston has shattered the front door in a drunken outburst. Arnulfo Maldonado’s scenic design presents a vast but messy kitchen — a wide open space, like the farm itself, perhaps once filled with promise, but fallen into disrepair. 

Emma’s older brother, Wesley — seemingly less wily, but smarter than his father thinks he is, and made compelling by a slow-burning Cooper Hoffman — has an even darker take on his mother’s suitor. “You think it’s Mr. and Mrs. America who’re gonna buy this place, but it’s not. It’s Taylor,” Wesley tells his sister, adding that the acquisition will mean “more than losing a house. It means losing a country. … It’s a zombie invasion. Taylor is the head zombie.” 

Taylor eventually gets his own, chilling monologue extolling the unbreakable might of the growing corporate and finance sectors. (One only wishes Shepard had lived long enough to take on big tech.) “The only thing you can do is … to play ball, to become part of us,” he tells Ella. Unfortunately, Kyle Beltran doesn’t inject enough unctuousness or menace into the role.

Under Scott Elliott’s vigorous direction, the leads fare better. Ms. Flockhart, who rose to fame playing the title character in the TV series “Ally McBeal” but has returned to the stage throughout her career, conveys both Ella’s suffering and her self-absorption. The actress has retained her delicate beauty, so that her character can seem almost doll-like, by turns sad and funny in her shallowness.

Mr. Slater, who was a teen idol in the late 1980s and early ’90s, proves just as deft mining the bleak humor and bitter poignance in the prematurely wasted Weston’s lines and antics. “I never saw my old man’s poison until I was much older than you,” he tells Wesley, explaining, ominously, “I saw myself infected with it.”

Mr. Slater’s exchanges with Mr. Hoffman are especially harrowing, both when Weston is mercilessly berating his son and later, when the father has a manic, ironic epiphany and suddenly becomes more generous, in his fashion.

By then, it’s too late for either of them, or for anyone else in the Tate family — including that sheep. The poison has been absorbed, and luckily for us, if not for them, it’s lost none of its potency.