Denver Brock and his son Aundra used to spend early mornings hunting rabbits in the wooded highlands of Harlan County, Ky. But they don’t get out there much these days. They both get too breathless trying to follow the baying hounds.

Instead, they tend a large garden alongside Denver Brock’s home. Even that can prove difficult, requiring them to work slowly and take frequent breaks.

“You get so dizzy,” Denver Brock said, “you can’t hardly stand up.”

The Brocks followed a long family tradition when they became Appalachian coal miners. For it, they both now have coal workers’ pneumoconiosis, a debilitating disease characterized by masses and scarred tissue in the chest, and better known by its colloquial name: black lung.

Mr. Brock, 73, wasn’t all that surprised when he was diagnosed in his mid-60s. In coal mining communities, black lung has long been considered an “old man’s disease,” one to be almost expected after