The Online Bin Packing Problem (OBPP) is a sequential decision-making task in which each item must be placed immediately upon arrival, with no knowledge of future arrivals. Although recent deep-reinforcement-learning methods achieve superior volume utilization compared with classical heuristics, the learned policies cannot ensure the structural stability of the bin and lack mechanisms for safely reconfiguring the bin when a new item cannot be placed directly. In this work, we propose a novel framework that integrates packing policy with structural stability validation and heuristic planning to overcome these limitations. Specifically, we introduce the concept of Load Bearable Convex Polygon (LBCP), which provides a computationally efficient way to identify stable loading positions that guarantee no bin collapse. Additionally, we present Stable Rearrangement Planning (SRP), a module that rearranges existing items to accommodate new ones while maintaining overall stability. Extensive experiments on standard OBPP benchmarks demonstrate the efficiency and generalizability of our LBCP-based stability validation, as well as the superiority of SRP in finding the effort-saving rearrangement plans. Our method offers a robust and practical solution for automated packing in real-world industrial and logistics applications.