Throughout his campaign for Kentucky governor, Matt Bevin, a Republican who won the election Tuesday, railed hard against the Affordable Care Act, promising to repeal the state’s expansion of Medicaid under the law. He has recently pulled back on that vow, saying he will instead freeze the program and prevent new enrollment. He may not be able to implement such a freeze — it would require a waiver from federal authorities, who will probably block it — but if he does get his way, a freeze is likely to eliminate health coverage for thousands of low-income people.

Although President Obama is very unpopular in Kentucky, the state was in many ways the great success story of his signature health care law. An additional 530,000 people, more than 10 percent of the state’s population, have enrolled in Medicaid since the program was expanded in 2014. That’s an 87 percent increase in average monthly enrollment from 2013, the largest percent change of any state. A little more than 600,000 people were enrolled on average each month in Kentucky in 2013, compared with 1.14 million as of August this year, according to the Centers for Medicare and Medicaid Services (CMS).

The state also had the largest decrease of any state in the percentage of uninsured people, which dropped from 14.3 percent of the population to 8.5 percent from 2013 to 2014, according to census data. In comparison, 12 percent of neighboring Tennessee’s residents remained uninsured in 2014, down just 1.8 percentage points from 2013. (Tennessee chose not to expand Medicaid.)

States can accept or reject Medicaid expansion, but if they take it, they have to follow federal rules. A few states, such as Arkansas and Pennsylvania, have been granted waivers that allowed experimental versions of the program, often letting states buy private insurance for recipients. It’s unlikely, however, that CMS would agree to a plan that caps coverage in any way, according to Robin Rudowitz, associate director of the Kaiser Commission on Medicaid and the Uninsured at the Kaiser Family Foundation. That’s probably because those kinds of caps have led to a decrease in coverage in the past.

Historically, low-income people have regularly moved on and off of Medicaid. About half of adults with a family income below 200 percent of the federal poverty line have a change in eligibility each year, according to a 2011 study by Benjamin Sommers, a professor of health policy and economics at Harvard University, who has studied both Medicaid churn and Kentucky’s recent success with health insurance enrollment.

“We don’t have good numbers yet on how often this [churn] is happening under the ACA,” Sommers said. “But historically, 50 percent of adults had a lapse in coverage during their first two years. So you’re talking about half a million people dropping insurance quickly.”

Evidence from Wisconsin and Arizona shows how freezing Medicaid can dramatically affect coverage over time, as people lose eligibility for the program but remain poor.

Wisconsin created a state Medicaid program for childless adults in 2009, before the ACA was a law. Within three months, the state was so overwhelmed by enrollment that it froze the program with just more than 65,000 participants. By July 2013, before enrollment was reopened under the ACA, that number had shrunk by 73 percent to just less than 18,000 people.

Similarly, when Arizona froze its Children’s Health Insurance Program (CHIP) in 2010, there were about 45,800 children in CHIP; 40,600 of those are no longer in the program. Although some of those children probably aged out or moved to other programs, the state did see a spike in the number of uninsured children.

Kentucky residents are waiting to see what approach Bevin takes. The state’s success in enrolling the uninsured has probably complicated his options: Hundreds of thousands of people would lose coverage if he dropped Medicaid expansion, and CMS is unlikely to allow rollbacks that make it difficult for people to access coverage.

CORRECTION (Nov. 11, 2:10 p.m.): An earlier version of this article misstated the drop in the uninsured population in Tennessee from 2013 to 2014. It dropped by 1.8 percentage points, not 1.9 percent.