RAJKOT, India—For nearly half a century, Laljibhai Gajjar ran factories making diesel engines and parts in and around this sleepy industrial city. But after Chinese products began swallowing up the market, he found another calling. He laid off 100 workers and started selling Hyundais.

Behind his bustling car showroom stands all that remains of his manufacturing operations: a crumbling workshop in which two dozen employees now assemble metal-stamping machines. Orders are dwindling. One of these days, Mr. Gajjar said, he’ll...