Sitting in a KFC restaurant in the former coal-mining town of Pomeroy, Ohio, a few hours before JD Vance addressed the Republican National Convention, Curtis Ramsey, 18, recalled the first time he heard the Ohio senator’s name.

It was last month, he said, in the Washington office of another Ohio Republican, Representative Jim Jordan.

Mr. Ramsey, who had never been to a big city or flown on an airplane before, was in the capital with two filmmakers seeking to draw attention to a new documentary, “Inheritance.” The film features Mr. Ramsey and examines the plight of drug-ravaged Appalachian communities like his own.

When the filmmakers, Matt Moyer and his wife, Amy Toensing, explained to Mr. Jordan what their documentary was about, the congressman broke into a smile. “Sounds like the story of the next vice president of the United States!” Mr. Jordan said.

Recalling this encounter, Mr. Ramsey bit into his chicken sandwich and considered the supernova trajectory of the “Hillbilly Elegy” author against his own precarious life.

“He was lucky,” Mr. Ramsey said of Mr. Vance, an Ohioan who spent time in his early years 165 miles southwest of Pomeroy in Jackson, Ky. “He got out.”