Mobile Edge Computing (MEC) is a technology designed for the on-demand provisioning of computing and storage services, strategically positioned close to users. In the MEC environment, frequently accessed content can be deployed and cached on edge servers to optimize the efficiency of content delivery, ultimately enhancing the quality of the user experience. However, due to the typical placement of edge devices and nodes at the network's periphery, these components may face various potential fault tolerance challenges, including network instability, device failures, and resource constraints. Considering the dynamic nature of MEC, making high-quality content caching decisions for real-time mobile applications, especially those sensitive to latency, by effectively utilizing mobility information, continues to be a significant challenge. In response to this challenge, this paper introduces FT-MAACC, a mobility-aware caching solution grounded in multi-agent deep reinforcement learning and equipped with fault tolerance mechanisms. This approach comprehensively integrates content adaptivity algorithms to evaluate the priority of highly user-adaptive cached content. Furthermore, it relies on collaborative caching strategies based on multi-agent deep reinforcement learning models and establishes a fault-tolerance model to ensure the system's reliability, availability, and persistence. Empirical results unequivocally demonstrate that FT-MAACC outperforms its peer methods in cache hit rates and transmission latency.