Wearable IMU–based fall detection systems often exhibit significant subject-specific biases, which can compromise their reliability for new users. This paper proposed a deployment-oriented approach to enhance cross-subject generalization by implementing independent z-score normalization at the subject level. Utilizing the KFall dataset with 32 participants and a lightweight ConvLSTM model, we evaluate conventional global normalization against our proposed per-subject scheme using a LOSO protocol. The results indicate that per-subject normalization provides modest yet consistent improvements, increasing precision from 95.86% to 96.45%, and F1-score from 96.30% to 96.59%. More importantly, it substantially tightens the distribution of cross-subject results, reducing the standard deviation of accuracy and F1-score by 34.9\% and 33.6\%, respectively, thereby mitigating the impact of low-performing outlier users and leading to more stable behavior across unseen subjects. Building on this observation, we present an on-device implementation workflow that leverages short calibration sequences to estimate user-specific normalization parameters, which are then stored and reused during inference. This proposed approach is deterministic, label-free, and computationally efficient, making it well-suited for resource-constrained wearable devices, such as those based on microcontrollers.