CHILLICOTHE, Ohio—Judy Sowers is the matriarch of a family that has seen generations work at “the Mead,” which is what many locals call the paper mill in Chillicothe.

On May 8, Sowers, two of her daughters, her brother, and her son-in-law gathered around a kitchen table in a house across the street from the mill and its red-and-white-striped tower.