Distance-based network localization is known to have solution, in general, if the network is globally rigid. In this technical note we relax this condition with reference to unit disk graphs. To this end, shadow edges are introduced to model the fact that selected nodes are not able to sense each other. We provide a localization algorithm based on such edges and a necessary and sufficient localizability condition. We also investigate the relation between the proposed approach and trilateration, showing from both a theoretical and empirical perspective that shadow edge localization succeeds also when trilateration fails.