If the Sacklers must keep paying state judgments, they “may be unwilling — or unable — to make the billions of dollars of contributions” outlined in the settlement, the Purdue lawyers wrote.

In a statement, members of the family said, “We remain committed to working with all attorneys general, cities, counties, towns and other parties to implement a resolution that provides meaningful resources and substantial funding to people and communities who need help now.”

Melissa B. Jacoby, a bankruptcy law expert at the University of North Carolina at Chapel Hill saw some logic to Purdue’s request . “It makes sense to ask for the bankruptcy court’s umbrella to be put over the Sacklers because Purdue is trying to argue that the family will maximize the value of the estate to the benefit of the creditors,” she said.

However, the Purdue lawyers contended, it is the states that would be responsible for blowing up the deal by continuing to pursue their cases against the company and family members.

A central part of the settlement involves restructuring Purdue into a public trust that would distribute the money from the sale of its drugs to the plaintiffs. But some legal experts said the new complaint is an effort to protect the Sacklers through the bankruptcy process even though they themselves are not filing for bankruptcy.

“The Sacklers don’t want to file for bankruptcy because that would expose all their finances as well as the transactions they made with Purdue,” Ms. Jacoby said, referring to the scrutiny required by such proceedings.

“The Sacklers want the benefit of bankruptcy without th e burdens of bankruptcy,” she said.

About two dozen states have sued the Sacklers or are planning to. They want to get at the family fortune, which they believe is more lucrative than anything the company could provide. Many of the states’ claims involve allegations that th e Sacklers improperly withdrew billions from Purdue for years. Letitia James, the New York attorney general, issued 33 subpoenas last month to banks and financial advisers who do business with the Sacklers. Last week, she announced that one of those subpoenas allowed her office to track a billion dollars that one family member had transferred from Purdue to previously undisclosed accounts.