The nearby mines shut down one by one. The cement business, once the city’s pride, waned. More than a dozen schools closed, as did one of the two movie theaters. The second would eventually follow.

By the time Kim Chang-gyu returned to Jecheon, South Korea, after four decades away to become the mayor, his hometown felt resigned to its decline. The town’s center was dotted with vacant storefronts, and local businessmen fretted about how tough it was to find workers.

Like many other small South Korean cities, Jecheon, cradled at the foot of two mountain ranges, is being eroded by rapid aging and rock-bottom birthrates. Other shrinking cities have tried offering money to entice newlyweds or free housing to parents of school-age children.

Mr. Kim, a retired diplomat, looked farther afield: Central Asia and the estimated half a million people of Korean descent who have been living there for nearly a century. If he could persuade enough of them to move to Jecheon — population 130,000 and shrinking — he thought they might lay the groundwork for its future.

Their forebears left the Korean Peninsula more than 100 years ago for the eastern edge of Siberia. In 1937, the Soviet Union, led by Joseph Stalin, rounded them up and deported them to what are now Uzbekistan, Kazakhstan and Kyrgyzstan.

Mr. Kim hoped that even if the language and historical connections had faded, the former Soviet Koreans would be more readily accepted than other migrant workers in a country that feels strongly about blood ties, he said.