PIKETON, Ohio—Through the trees around her home, Elizabeth Lamerson can see part of the 70-year-old uranium-enrichment plant that government contractors plan to start tearing down this week. In this small Appalachian community, she and many of her neighbors say they are worried about any escape of radioactive material and the impact it could have on their health.

Ms. Lamerson and her husband believe trace amounts of uranium detected in their attic in 2019 came from the nearby plant. They want a tent or enclosure put around the buildings as they are taken down, and the couple also oppose a plan to store waste locally.

“It’s provided jobs and a lot of people continue to work there,” said Ms. Lamerson, who worked at the plant from 2007 to 2014. “What I’m against is open-air demolition and not storing waste properly.”