TIRUPPUR, India — If the tag on your T-shirt says “Made in India,” there’s a good chance it came from this southern industrial hub — long known as “Dollar City” for its dominance in the U.S. market. Now, just seven weeks after the Trump administration imposed a 50 percent tariff on Indian exports, many of Tiruppur’s garment factories have ground to a halt. The slowdown has rippled through a vast network of hulking plants and small workshops, which employ more than 600,000 people. Thousands of fabric cutters, thread trimmers and sewing machine operators are suddenly out of work. “Production has...