This paper proposes a neural-network-based framework using Convolutional Neural Network and Long-Short Term Memory (CNN-LSTM) for detecting faults and recovering signals from Hall sensors in brushless DC motors. Hall sensors are critical components in determining the position and speed of motors, and faults in these sensors can disrupt their normal operation. Traditional fault-diagnosis methods, such as state-sensitive and transition-sensitive approaches, and fault-recovery methods, such as vector tracking observer, have been widely used in the industry but can be inflexible when applied to different models. The proposed fault diagnosis using the CNN-LSTM model was trained on the signal sequences of Hall sensors and can effectively distinguish between normal and faulty signals, achieving an accuracy of the fault-diagnosis system of around 99.3% for identifying the type of fault. Additionally, the proposed fault recovery using the CNN-LSTM model was trained on the signal sequences of Hall sensors and the output of the fault-detection system, achieving an efficiency of determining the position of the phase in the sequence of the Hall sensor signal at around 97%. This work has three main contributions: (1) a CNN-LSTM neural network structure is proposed to be implemented in both the fault-diagnosis and fault-recovery systems for efficient learning and feature extraction from the Hall sensor data. (2) The proposed fault-diagnosis system is equipped with a sensitive and accurate fault-diagnosis system that can achieve an accuracy exceeding 98%. (3) The proposed fault-recovery system is capable of recovering the position in the sequence states of the Hall sensors, achieving an accuracy of 95% or higher.