The high-risk programs offered a separate insurance pool for people with potentially expensive medical conditions. The idea is that by separating sick people from the majority of people who are healthy, insurers could offer cheaper rates to the healthy people. Insurers could charge higher prices to those with existing medical conditions, but they would also rely on other sources of funding, including from the government, to cover their costs.

The system worked for Dan Nassimbene and his wife, who had breast cancer but is in remission. They enrolled in Colorado’s high-risk pool for three years. She paid about $375 a month for a plan that covered most of her treatments.

In 2014, though, the high-risk pool was closed, and Mr. Nassimbene bought a plan that met the requirements of the Affordable Care Act. The cheapest plan he could buy for himself and his wife cost around $900 a month and came with a family deductible of around $12,000, much higher than it was before. His income was too high for him to receive any government subsidies, which help about 80 percent of people buying such plans.

“I had coverage but no access,” said Mr. Nassimbene, 55. He has since switched to a Christian health care sharing ministry, in which members cover one another’s medical bills. It does not qualify as coverage under the law.

In many cases, the high-risk pools were overburdened financially, leaving many people without insurance or with tight restrictions on coverage. Insurers refused to cover the individuals who were likely to have the highest expenses, like those who had H.I.V. or serious kidney disease, and the pools lost money.

Many states had to turn applicants away — in some states, only a small percentage of those who applied received coverage — and the insurance was sharply limited to control spending.