When her small executive search firm in New York City canceled its health insurance policy last year because of the recession and rising premiums, April Welles was able to buy her own plan and still be covered for her cancer and multiple sclerosis.

She was lucky to live in New York, one of the first states to require insurance companies to offer comprehensive coverage to all people regardless of pre-existing conditions. But Ms. Welles, 58, also pays dearly: Her premium is $17,876 a year.

“That’s a lot of groceries,” she said.

New York’s insurance system has been a working laboratory for the core provision of the new federal health care law — insurance even for those who are already sick and facing huge medical bills — and an expensive lesson in unplanned consequences. Premiums for individual and small group policies have risen so high that state officials and patients’ advocates say that New York’s extensive insurance safety net for people like Ms. Welles is falling apart.

The problem stems in part from the state’s high medical costs and in part from its stringent requirements for insurance companies in the individual and small group market. In 1993, motivated by stories of suffering AIDS patients, the state became one of the first to require insurers to extend individual or small group coverage to anyone with pre-existing illnesses.