Then, as the 2008 financial crisis set in, rents, instead of going up, went down. To pay off some of their debt, the Kushners began selling parts of the building, including its most valuable asset, the retail space on Fifth Avenue, to the Carlyle Group and Crown Acquisitions for $525 million, a remarkable price. The proceeds were used to pay off secondary loans on the building, not the main mortgage.

But the bleeding continued. Two years later, with the tower’s reserve funds nearly exhausted and the owner losing as much as $30 million, the mortgage holder appointed a “special servicer” to oversee 666 Fifth Avenue. Such a company manages a property loan when the borrower is in danger of falling into default.

The Kushner Companies renegotiated the terms of the loan in 2011.

At the same time, Vornado, a publicly traded real estate company and one of the city’s largest landlords, bought 49.5 percent of the building’s office space for $80 million and other financial pledges as part of refinancing the property. In 2013, it bought the retail condominium from Crown and Carlyle for $707 million, except for a portion that had been sold to Zara, the Spanish clothing chain.

Vornado’s chairman, Steven Roth, declined to comment on the building. His firm has veto power over any deal, according to its loan agreements with the Kushner Companies.

The $1.2 billion mortgage on 666 Fifth Avenue has swelled to $1.4 billion with accrued interest, according to financial records filed by Vornado. Revenue, which continues to decline, covers only 66 percent of the building’s debt obligations, according to the latest report by Trepp.

At this point, the value of the office space is less than the mortgage, said Jed Reagan, a commercial real estate analyst at Green Street Advisors, a real estate research firm based in California. “There is no equity value” on the office portion of the building, he said.

The Kushners have not filled space as it opens up because they plan to demolish the aluminum-clad building. More than two years ago, when the market for superluxury condominiums and high-end retail was hot, they commissioned Ms. Hadid, a star architect who died last year, to design a residential and hotel tower sitting atop a base of high-end shopping to replace it.