A year ago this month, I caught the New York premiere of a gorgeous, devastating play narrated by a wolf — that is, a young adult actor portraying a 6-year-old child who has, for practical reasons, assumed the identity of a wolf. In “Wolf Play” — being produced again by Soho Rep in collaboration with Ma-Yi Theater Company, this time presented by MCC Theater — the fourth wall comes down hard and fast, the moment this lupine figure leaps out without warning and utters the first line: “What if I said I am not what you think you see.”

Playwright Hansol Jung punctuates the sentence with a period; it is a statement, not a question. The miracle of “Wolf Play” is how Ms. Jung and director Dustin Wills rattle our emotions and pierce our hearts even as they remind us, regularly and often flamboyantly, that they’re spinning a fictional tale. If anything, the new staging, which features a tweaked text and a couple of different actors, feels more urgent in its mission to beguile while relaying hard truths.

The story is at once outrageous and sadly credible. It centers on the 6-year-old, Jeenu, a Korean boy whose adoptive American parents have decided, after having a biological child of their own, to try to place him with another couple. (Yes, people do such things; search “rehoming” if you need proof.)

The exchange is facilitated, like so many that have negatively affected minors in recent years, by the internet. Jeenu’s guardians alert a Yahoo group, and Robin, a married woman desperate for a child but stymied by other channels for various reasons, replies in good faith. As the play opens, Jeenu’s adoptive father, Peter, is delivering the boy to Robin’s home, rather as one would drop off a sofa. 

Jeenu enters with wrenching hesitancy — a quality made even more poignant, as many of the boy’s actions and reactions will be, by the presence of a spare but winsome puppet, designed by Amanda Villalobos. Maneuvered by Mitchell Winter, reprising the role of narrator and child, the puppet is by turns a shield and a means of expressing all manner of feeling — anger, affection, curiosity, defiance, despair.

As the play progresses, Mr. Mitchell, executing his dual role with a perfect balance of sensitivity and spry charisma, occasionally relinquishes the puppet to other cast members to reflect Jeenu’s developing relationships with their characters. An especially strong bond is forged between the boy and Robin’s non-binary spouse, an aspiring boxer named Ash, who initially doesn’t share their partner’s maternal yearning.

Jeenu and Ash are drawn together as two people who have been marginalized, forced to grow tough skin as they’ve sought out families that would finally embrace them. Another returning cast member, Esco Jouléy, movingly conveys both Ash’s burnished armor and the tenderness that Jeenu mines in him, whether they’re sharing cold cereal or the boy is asking his new kindred spirit to howl in unison. Plainly, Ash can relate to Jeenu’s experience as a “lone wolf” fighting to survive, as the boy repeatedly describes it.

Ash’s wife seems less intimidating on the surface; as Jeenu observes, “Robins are a very delicate species. They don’t like to fight.” But this Robin — captured in a lovely, fraught performance by Nicole Villamil, also revisiting the role — will do so when pressed, as she eventually is by both Peter and her brother, Ryan, who as Ash’s longtime trainer isn’t thrilled about the increasingly consuming role the kid has in his client’s life.

Peter and Ryan are played by two actors new to the production, Christopher Bannow and Brian Quijada, who gamely embody that member of the animal kingdom suggested by both characters: the weasel. Ms. Jung doesn’t bang the audience over the head with tirades about toxic masculinity; instead, she reveals these pathetic men-children by having them repeatedly and simultaneously whine to the women who at once control and enable them — Peter’s wife and Ryan’s mother (neither of whom we meet) — until you wish the wolf would just have at them.

Not surprisingly, though, this wolf will turn out to be as vulnerable as he would like to be ferocious. In the heart-stopping moments before his fate is disclosed, the narrator of “Wolf Play” essentially gives audience members the option of leaving the theater. “Don’t you sometimes, just wanna walk out?” he says bluntly, adding, “You know it’s not real … but sometimes it feels so real.”

The clever wolf knows, of course, that he is making this offer in vain. Because the difference between having your heart broken by life and having it broken by art is that the latter — if done with flair and care, as it certainly is here — is almost always well worth it.