In Industrial Internet of Things (IIoT) systems, predictive maintenance (PdM) requires precise and timely failure prediction on devices with limited resources. By deploying machine learning models directly on IIoT edge devices, Tiny Machine Learning (TinyML) eliminates dependency on the cloud and lowers latency. However, lightweight machine learning techniques are needed to achieve high predictive performance under rigid memory, power, and computational constraints. The state-of-the-art in lightweight machine learning for PdM is thoroughly reviewed in this paper, which covers knowledge distillation, TinyML frameworks, automated techniques (AutoML/NAS) for model optimization, and model compression approaches (pruning, quantization, weight sharing). We examine how these methods are used in industrial PdM use cases, examine the trade-offs between accuracy and model size, and provide a comparative analysis of deployment feasibility, accuracy impact, and compression efficiency. Recent research findings show that carefully compressed models can operate on microcontroller-class devices in real time with little loss of accuracy. We also outline future research directions and address issues unique to TinyML-based PdM, such as data imbalance, real-time constraints, and energy efficiency. The categories and insights offered are meant to help professionals and academics create effective on-device predictive maintenance solutions for Industry 4.0.