Thruster faults are one of the most common malfunctions encountered during Unmanned Underwater Vehicle (UUV) missions. This type of fault can lead to unwanted behaviour and jeopardise the UUV mission. Successful thruster fault management depends on accurate diagnostics. However, some scenarios, particularly instances of thruster faults due to external factors, pose a hard diagnostic task. This is particularly challenging in the context of abnormal behaviours that are detected but no fault diagnosis can be provided by the onboard fault management system. This type of fault is called nondiagnosable and it is the main target of this work. The aim of this paper is to propose a solution for controlling UUVs subject to non-diagnosable thruster faults using a Deep Reinforcement Learning (DRL)-based approach. This paper provides a comparison between an end-to-end DRL-trained controller and a standard PID controller to overcome partial and total thruster faults of a UUV. The consistency and robustness of the proposed method is verified by simulations. The results demonstrate the DRL-based controller's effectiveness in addressing nondiagnosable thruster faults that would otherwise hinder the successful completion of the mission.