Stubborn steel capacity is also causing friction with Washington. Both the United States and the European Union are up in arms over a flood of cheap steel pouring into global markets from excess Chinese factories. In response, Washington has slapped steep tariffs on some Chinese steel imports.

“Implementing policies to substantially reduce production in a range of sectors suffering from overcapacity, including steel and aluminum, is critical to the function and stability of international markets,” the United States Treasury secretary, Jacob J. Lew, said during a Beijing visit this week.

Songting — which employed about 6,000 workers, according to the local government’s website — was among the larger, privately owned mills in town. But with construction of new homes and infrastructure in the doldrums, prices of steel plunged, and Songting, along with the entire industry, began to suffer. Workers say they stopped receiving regular paychecks in early 2015. A section of the plant was idled for part of the year, and management began laying off staff.

One of the unfortunate was C. F. Shi, 45, who worked in Songting’s factory for 21 years and asked that her full name not be used. One morning last September, she arrived at the plant to find her boss dropping folded slips of paper into a box. As the box was passed around the room, each worker had to draw a slip, and only those who selected one with a mark on the inside could stay on the job.

Ms. Shi lost out in the lottery and got sent home, without five months of unpaid wages or severance. She was distraught. “I even thought of trying to hang myself,” she said.