While the deal relieves some of the Kushners’ troubles, difficulties persist across their real estate empire, at least in part because of their connection to the White House. “If you do business with the Kushners, there’s a headline reality,” said Kenneth Pasternak, executive chairman of the real-estate firm KABR Group and an investing partner of the Kushner family in multiple developments. “I don’t want to say it’s a headline risk,” he added. “There’s a headline reality.”

In the 666 Fifth Avenue deal, Brookfield paid about $1.1 billion in upfront rent, according to an executive who requested anonymity because he had been briefed on the deal but was not authorized to discuss it. Charles Kushner, Jared’s father, who now runs the company, in turn, negotiated with his lenders to pay less than the company owed to satisfy the debts, the executive said.

Analysts have long said that 666 Fifth was worth less than its debts. The building was 30 percent vacant and only generated about half the annual mortgage payments. In recent months, the building’s largest remaining tenant, Millennium Management, signaled that it too planned to leave.

A spokeswoman for Kushner Companies declined to comment on the Brookfield deal.

The purchase of the aluminum-clad tower was intended to vault the Kushners into the top ranks of New York real estate from their perch in New Jersey, where they were known for a huge portfolio of garden apartment complexes. They moved their company headquarters to 666 Fifth, from where they presided over a new and rapidly expanding empire that included former industrial buildings in Brooklyn, apartments in Maryland and development sites in Jersey City, N.J.

But they ran into trouble almost immediately. They were unable to get the office rents they expected in 2007, making it difficult to pay the initial $1.75 billion debt on the building. Then the recession hit.