“It would require changing into something people wouldn’t recognize as scouting,” said Mr. Kosnoff, noting the organization’s history of sending boys on remote outings with volunteer leaders.

Over the span of a century, more than 130 million Americans have participated in the Boy Scouts. But membership has been dwindling in recent decades, as shifting American attitudes pulled many families away from the God-and-country oaths and outdoorsy survival skills that the Scouts offered. Then, in more recent years, lawsuits brought to light a long history of sexual abuse problems that the organization strove to keep secret.

The Boy Scouts have kept internal files about abuse cases at their headquarters almost since the group was founded in 1910. In a 1935 article in The New York Times, the organization described having files on hundreds of people who had been scout leaders but had been labeled “degenerates.” In recent years, an expert hired by the organization reviewed decades of records and reported that there were nearly 8,000 “perpetrators.”

The Boy Scouts fought the release of some of the files in an Oregon case, in which a jury held the Scouts liable in 2010 for $18.5 million in punitive damages. Two years later, the Oregon Supreme Court ordered that the records in that case be made public.

Paul Mones, a lawyer for the plaintiffs in the Oregon case, expressed concern on Tuesday that the Boy Scouts’ bankruptcy filing would rob other victims of the opportunity to hold the group accountable in court. “The justice that they so well deserved will unfortunately escape them in the end, and that is a true tragedy,” he said.

The Boy Scouts said in April 2019 that every account of suspected abuse in the group’s files had been reported to law enforcement, and that it had never knowingly allowed people who harm children to work with them. The group later acknowledged that decades before, some volunteers who were credibly accused of abuse had in fact been allowed to return.

“We are outraged that there have been times when individuals took advantage of our programs to abuse innocent children, and sincerely apologize to anyone who was harmed during their time in Scouting,” Mr. Turley wrote in his statement on Tuesday. After years of implementing measures like mandatory background checks for volunteers and a ban on one-on-one interactions between adults and youths, he said, “Scouting is now safer than ever before.”