The changes to tighten enrollment and collect unpaid premium payments aim to cut down on signups from people after they are sick, which insurers say has created an unprofitable mix of healthy and sick customers.

Humana Inc on Tuesday said it was pulling out of this market altogether for 2018 and Anthem Inc. and Aetna Inc have said that without changes, they might not take part after 2017.

President Donald Trump and congressional Republicans campaigned last year on a promise to scrap the 2010 healthcare law that is a key legacy of Democrat Barack Obama’s presidency. But they are struggling to agree on a replacement for the law, which enabled up to 20 million previously uninsured Americans to obtain health coverage.

The proposed new rule, issued by part of the U.S. Department of Health and Human Services, sets out changes that are meant to shore up the system developed under Obamacare. It is unclear which elements of this system could survive in the Republican replacement.

They come as the administration backed off implementing tougher oversight of the individual mandate, the requirement for all Americans to have health insurance or pay a fine, that was due to go into effect for 2016 taxes. That rule was supposed to help balance the pool of healthy and sick but some insurers say it has not worked as intended and Republicans have said they will overturn it.

Shares of insurers were slightly higher on Wednesday morning with Aetna gaining 1.8 percent to $128.12, Cigna up less than 1 percent at $147.40 and Humana up 1.7 percent to $209.47. Anthem fell less than 1 percent to $162.98.

The U.S. Internal Revenue Service will not reject tax filings for the year 2016 that fail to indicate whether they had health coverage or paid the penalty set under Obamacare, the IRS said in a statement. This change is a result of Trump’s executive order to reduce the regulatory burden of the law when possible and is a return to the policy that was in place for 2015 taxes, the IRS said.

The Centers for Medicare & Medicaid Services, part of the U.S. Department of Health and Human Services, on Wednesday proposed the new rule that includes verifying the status of people enrolling in the plans.

The rule also proposes insurers can collect unpaid premiums from members when they sign up with the same issuer again, with the goal of establishing an incentive for continuous coverage.

“These proposals would help stabilize the current individual market and are a good start toward improving the functioning of the marketplace, so that any longer-term reforms can begin on a better footing,” said Alissa Fox, a senior vice president of Blue Cross Blue Shield, a major player on the exchanges.

Caroline Pearson, a senior vice president at the healthcare consultancy Avalere Health, said the rule is meant to encourage plans to participate in 2018 but that it is unclear if “these changes will be sufficient to ensure all regions of the country have an exchange operating in 2018.”

The rule proposes shortening the upcoming annual open enrollment period for the individual market to Nov. 1 through Dec. 15. The change will align the marketplaces with the employer-sponsored insurance market and Medicare.

Aetna CEO Mark Bertolini on Wednesday said during a Wall Street Journal forum that the Obamacare exchanges had entered a “death spiral” in which rising premiums pushed out the healthiest customers, which in turn raises rates.