(Mr. VanSickle and his wife could be eligible for thousands of dollars in subsidies if they purchased insurance under the Affordable Care Act, said Larry Levitt of the Kaiser Family Foundation. But such a plan would most likely be more limited, and Mr. Trump still maintains that he wants to undo the program.)

The miners typically regard their health care with a sense of moral entitlement, having frequently passed up higher pay during contract talks in order to top off their benefits.

John Leach, 67, worked in four different mines over 23 years as a miner in western Kentucky. As a result, he said, “I got four of those speeches: ‘If you work here, you work your 20 years, you are guaranteed insurance for yourself and your family for the rest of your life.’”

Since he retired in 2001, that insurance, along with Medicaid and Medicare, has kept him and his wife, Rhonda, 60, afloat. The couple care for two adult children with severe physical and mental disabilities. In 2015, the health plan paid out over $50,000 for Rhonda’s hip-replacement surgery.

“I don’t know if you’ve ever gone through a serious test at the doctor’s office,” Ms. Leach said by phone. “You wait and wait and don’t hear anything and the pressure starts building up: Am I going to live or am I going to die? That’s exactly what this is like: living and dying.”

Many retired miners who supported Mr. Trump understood that his promise to revive employment in their industry was a long shot in the face of cheap natural gas — “a couple of jobs” might come of it, Mr. VanSickle said.