Feedback-controlled electric breakdown of graphene in air or vacuum is a well-established way of fabricating tunnel junctions, nanogaps, and quantum dots. We show that the method is equally applicable to encapsulated graphene constrictions fabricated using hydrogen silsesquioxane. The silica-like layer left by hydrogen silsesquioxane resist after electron-beam exposure remains intact after electric breakdown of the graphene. We explore the conductance switching behavior that is common in graphene nanostructures fabricated via feedback-controlled breakdown, and show that it can be attributed to atomic-scale fluctuations of graphene below the encapsulating layer. Our findings open up new ways of fabricating encapsulated room-temperature single-electron nanodevices and shed light on the underlying physical mechanism of conductance switching in these graphene nanodevices.