Localizability in large-scale, randomly deployed Wireless Sensor Networks (WSNs) is a classic but challenging issue. To become localizable, WSNs normally require extensive adjustments or additional mobile nodes. To address this issue, we utilize occasional passive events to ease the burden of localization-oriented network adjustment. We prove the sufficient condition for node and network localizability and design corresponding algorithms to minimize the number of nodes for adjustment. The upper bound of the number of adjusted nodes is limited to the number of articulation nodes in a connected graph. The results of extensive simulations show that our approach greatly reduces the cost required for network adjustment and can thus provide better support for the localization of large-scale sparse networks than other approaches.