At Playwrights Horizons, the new James Lapine play “Fran’s Bed” poses one of the gripping, controversial questions of our time: When, for the greater good, do we turn off life support? Should it be when a show performs underwhelmingly out of town? Should artistic director Tim Sanford have flipped the switch? Or could director-playwright Mr. Lapine have stifled this creation in its crib? Whatever your thoughts on mercy killings, this shoddy, offensive, shallow show will make you desperate to put “Fran’s Bed” out of our misery.

On its surface, Mr. Lapine’s script pretends at complexity. Though Fran (Mia Farrow) lies before us in a coma, her mind seems alive and well. At least, she’s busy having flashbacks and wafting around her hospital room. All the rushing back and forth in time, though, only convinces us that Fran can’t make a decision (literally) to save her life. Finally, after an hour and 45 minutes of her mewing self-pity, the choice to stay or go is no longer up to her. In a post-Terri Schiavo world, obviously the questions of life, death, and family responsibility weigh heavily on us all. Inspiring homicidal feelings in an audience, however, can’t be the best way of asking them.

Fran’s family, waddling under the weight of a thousand cliches, surrounds their dying mother. Some want to detach her feeding tube. They all wonder about her internal state. Various publicity materials refer to the piece as a comedy, so each character arrives fresh from the sitcom catalog. The two daughters, Julia Stiles as career-driven Birdie and Heather Burns on the mommy-track, scuffle half-heartedly over their opposing priorities. Their father (Harris Yulin, embarrassed to be there) hasn’t understood his wife in years. And Dolly (Brenda Pressley), Fran’s nurse, carries a Bible, comes from “the Islands,” and watches (wait for it!) “Touched by an Angel.” Who will fight the “Do Not Resuscitate” order with preachy invasiveness? One guess.

Fran’s last weeks on earth reflect the emptiness of the years she spent awake. Her fantasies all revolve around meeting with psychologists – those who cosset her, chide her for taking too much pain medication, and try to goose her out of bed. The title character (the bed, not Fran), dominates the stage – often as the hospital cot, occupied by a rubber-dummy of Mia Farrow, but it can also become the California king that Fran rarely left back at home. Hers is a cruel stereotype: the whining, damaged, clinically depressed housewife. Profoundly disaffected and totally spaced out, she prefers to spend her life under the covers. It’s a peculiar choice, to make a “right-to-death” play out of a character who has always refused to live.

Mr. Lapine doesn’t bother to explain what wrecked his central character’s psyche, despite showing us a few cringe-inducing flashbacks. The worst of them forces Mr. Yulin to abandon the rest of his dignity while re-enacting a college sorority mixer. If Mia Farrow’s post-lobotomy air seems appropriate for Fran’s decline, it’s totally bizarre when she pretends to be her younger self. Her performance does have a kind of train-wreck appeal: Her skin lets off a kind of radioactive glow, and her eyes bat like giant moths. But her pleading, sugary tone never changes – and 90 minutes with her feels like more than a lifetime.

Ms. Farrow isn’t the only one who fails to transition from screen to stage; Ms. Stiles squeaks in under the already low bar. Ms. Stiles looks like someone slapped her backstage with a fish – her face assumes an appalled expression at the get-go and then never moves. She delivers racist jokes (Mr. Lapine thinks men named Jorge shouldn’t wear gold chains … hilarious!) and emotional breakdowns with no variation, all without moving her mouth. She may not belong in the theater, but she has a bright future in ventriloquism.

Unfortunately, a few excellent actors do get trapped in this sticky mess. Ms. Burns tries to match Fran’s needy whine, projecting a future in which her character will fall prey to her mother’s neuroses. Marcia DeBonis tries to pump up her jokes as a frazzled hospice administrator – only in her scenes does assisted dying seem like a grand topic for a farce. But it’s a farce we never see. Mr. Lapine settles instead for a Hallmark movie of the week, with self-consciously quirky touches. In one of Fran’s coma-dreams, her hospital television rotates, and we see a mock soap opera with Ms. Farrow in the leading role. Frankly, they can’t stand the competition. When a theater piece fails to beat out “General Hospital” for emotional depth, it’s definitely time to pull the plug.

Until October 9 (416 W. 42nd Street, between Ninth and Dyre Avenues, 212-279-4200).