Seven months after the Supreme Court struck down a deal that would have resolved thousands of opioid cases against Purdue Pharmaye7, the company’s owners, members of the Sackler family, have increased their cash offer to settle the litigation — but with a novel catch.

Under the framework for a new deal, the Sacklers would not receive immunity from future opioid lawsuits, a condition that they had long insisted upon but that the court ruled was impermissible.

Instead, they would pay up to $6.5 billion — $500 million more than the previous agreement — but with a new condition: Claimants, including states, municipalities and individuals, would have to set aside as much as $800 million in an account akin to a legal-defense fund for the billionaires to fight such cases, according to people familiar with the negotiations.

Some details of the framework — but not the legal-defense fund — were announced on Thursday by the New York attorney general,PHL63 Letitia James. She said the overall settlement totaled $7.4 billion, which would include $897 million from Purdue.

New York could receive as much as $250 million, she said.

“The Sackler family relentlessly pursued profit at the expense of vulnerable patients and played a critical role in starting and fueling the opioid epidemic,” Ms. James said.

Echoing other settlements in nationwide opioid litigation, these payments are intended to fund efforts to prevent and treat addiction in hard-hit communities across the country.

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The accountability office said many of those systems “have critical operational impacts” on air traffic safety and efficiency. Many of them are also facing “challenges that are historically problematic for aging systems,” according to the report.

Robinson’s history of comments that have been widely criticized as antisemitic and anti-gay made him a deeply polarizing figure in North Carolina long before his bid for governor was upended last week by a CNN report that he had called himself a “Black NAZI” and praised slavery while posting on a pornographic website between 2008 and 2012. Now, some of his allies are abandoning him. Most of his senior campaign staff members have resigned. The Republican Governors Association said that its pro-Robinson ads would expire tomorrow and that no new ones had been placed. And former President Donald Trump, who endorsed Robinson in the spring, calling him “Martin Luther King on steroids,” did not mention him once during his rally in the state over the weekend.

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