Given fixed Bartnik data, one may ask whether there exists a compact manifold with nonnegative scalar curvature that induces the given Bartnik data on its boundary. We generalize this question to consider fill-ins that need not be compact, but rather need only be complete or have “scalar curvature shields,” and we explain how to generalize some of the known nonexistence results for compact fill-ins to noncompact fill-ins. The main technical ingredient involves generalizing Pengzi Miao’s work on Riemannian manifolds admitting corners along a hypersurface that have nonnegative scalar curvature in a weak sense. This is joint work with Martin Lesourd and Ryan Unger.