In recent years, the integration of prediction and planning through neural networks has received substantial attention. Despite extensive studies on it, there is a noticeable gap in understanding the operation of such models within a closed-loop planning setting. To bridge this gap, we propose a novel closed-loop planning framework compatible with neural networks engaged in joint prediction and planning. The framework contains two running modes, namely planning and safety monitoring, wherein the neural network performs Motion Prediction and Planning (MPP) and Conditional Motion Prediction (CMP) correspondingly without altering architecture. We evaluate the efficacy of our framework using the nuPlan dataset and its simulator, conducting closed-loop experiments across diverse scenarios. The results demonstrate that the proposed framework ensures the feasibility and local stability of the planning process while maintaining safety with CMP safety monitoring. Compared to other learning-based methods, our approach achieves substantial improvement.