Henry W. Fust of Fust Charles Chambers, a Syracuse firm that provides accounting services to hospitals across New York State, said that for hospitals to “go totally naked” was very unusual and “would draw into question the viability of the entity.” It would also be difficult for any patient to recover money from hospitals like Wyckoff and Interfaith, which are already deeply in debt. “You can’t get blood out of a stone,” Mr. Fust said.

An absence of insurance is generally a sign of double trouble, signifying that rates have gone up because of high claims. Many commercial insurance companies pulled out of New York years ago because “this is a very litigious state, high severity and high frequency,” said Edward J. Amsler, vice president of Medical Liability Mutual Insurance Company, which is owned by its policyholders. Financially stable hospitals have responded by banding together in groups like Mr. Amsler’s, setting premiums and reserves and sometimes sharing risks. (Lenox Hill has primary liability coverage through this company, setting aside reserves for larger claims.)

“If you were on the board of a public corporation, and you had director responsibility, and if it was a health care corporation, you would damn well demand that the management of that hospital was properly insured,” said Stephen Berger, the head of a state task force on ailing Brooklyn hospitals, which recommended that Interfaith and Wyckoff Heights merge with a stronger hospital.

“You wouldn’t let somebody pick up a Q-tip if you weren’t comfortable with the level of malpractice, liability, fire, coverage, everything else that you had in that hospital, because you would have liability if you failed to perform your true duties.”

Some hospital executives say, however, it is better to be effectively uninsured, because lawyers follow the money.

“Malpractice insurance is a lawsuit magnet,” said a former hospital administrator who did not want to be named to avoid upsetting potential employers. Malpractice lawyers said that underinsured hospitals put them in a tricky position.

“There is some arm-twisting,” said Alan Fuchsberg, a personal injury lawyer in Manhattan, as plaintiffs are told that they will end up with nothing and push the hospitals into bankruptcy if they do not “just take the little bit” that is offered to them.