TANGSHAN, China—The wheels are coming off the world’s biggest auto market after decades of blistering growth, as a prolonged and unprecedented sales slump partly induced by policy changes closes thousands of dealerships, idles factories and weighs on an already slowing economy.

In Tangshan, a city of about 7.6 million in the country’s north known for its steel producers and heavy industry, around five of the 30 dealerships in the Lunan Car Culture Industrial Park have closed in the past year, dealers said. Abandoned furniture...