RICHMOND, Va. — At the William King Museum in the heart of Appalachia, a panel of 16 small paintings depicting water mills along the region’s landscape is deteriorating, and along with it, important chronicles of southwest Virginia’s rural culture.

The series of canvases taped to flimsy wood paneling is flaking and curators at the Abingdon museum are hoping to conserve it through a program has helped some of those previously involved apply for grants and help with fundraising efforts....