To address the challenges of vibration control in flexible systems, an active fault-tolerant control framework utilizing dual-mode Model Predictive Control (MPC) is introduced. This advanced approach integrates fault detection, isolation, and accommodation mechanisms directly into the control system to ensure continuous and reliable operation in the presence of soft sensor faults, minimizing performance degradation and safeguarding system integrity. The framework leverages the predictive capabilities of MPC and the dual-mode stability concept to achieve an optimal balance between active vibration suppression and fault accommodation. In this framework, dual-mode MPC is particularly advantageous for managing system constraints, offering better adaptability to uncertainties and unexpected disturbances compared to traditional controllers. A detailed evaluation using a Smart Flexible Beam (SFB), employed as an active vibration isolation system, highlights the superior performance of dual-mode MPC. It outperforms standard MPC by providing enhanced fault tolerance in scenarios involving soft sensor failures and offers better constraint-handling capabilities than Linear Quadratic (LQ) controllers. Furthermore, dual-mode MPC demonstrates robustness to parametric variations and ease of tuning, making it a versatile and effective solution. Through comprehensive simulation studies, the proposed framework showcases its efficacy in achieving significant vibration attenuation, maintaining system stability, and ensuring operational reliability, particularly for critical applications such as aerospace. This makes it a promising approach for enhancing the resilience and robustness of smart flexible systems in high-performance environments.