Owners of such apartments are reluctant to discuss their situations, aware that the label of hoarder invariably carries a stigma. Some are aware that the state of their living space has spiraled out of control. Others are in denial.

For brokers, showing and marketing a true hoarder property can require considerable creativity. Some spaces are firetraps and home to bugs or worse, with rooms so jampacked that visitors must navigate sliver-thin passages simply to move from one to another. Online visuals present a special challenge; a broker might display a floor plan, a view out a window or another apartment on the same line.

And forget the open house. Sometimes prospective buyers can’t get past the front door. Buyers must also be encouraged to picture the rosy possibilities that await them once the junk has been carted away and the contractors have worked their magic. As brokers invariably recommend, “Close your eyes and pretend.”

The possibilities are considerable, because many of these spaces are trophy homes or used to be. “Some of the best addresses in New York City have hoarders in them,” said Harold Kobner of Argo Real Estate, who last winter sold a Classic 7 owned by a hoarder on the Upper West Side. Despite the legal and financial tangles that often complicate such sales, these properties spark bidding wars and attract dozens of potential buyers, some making all-cash offers well above the asking price.

“Right now people are starving for anything,” said Mark D. Friedman, a Halstead broker who sold his first hoarder apartment, home to three dogs, eight cats and “not a speck of ground without something on it” eight years ago. “They’ll look past a lot to see the bones of a place.”

Robin Plevener, a Citi Habitats broker, discovered both the challenges and the rewards of selling a hoarder’s apartment last year when she sold a two-bedroom on East 86th Street, home since the 1950s to a quilter unable to discard so much as a scrap of fabric.

“It was a fabulous building with a strict board,” Ms. Plevener said, “but the apartment was literally overflowing with hundreds of pounds of material that the owner used for her work.” Dozens of full-size quilts were stashed in the bedroom. The dining table was buried beneath acres of silk, satin and calico. The five walk-in closets were packed so full that their doors hadn’t been shut in years. The door to the room used as a studio had to be kept closed, for fear the owner’s cats would get lost in the clutter.