In the realm of sustainable IoT and AI applications for the well-being of elderly individuals living alone in their homes, falls can have severe consequences. These consequences include post-fall complications and extended periods of immobility on the floor. Researchers have been exploring various techniques for fall detection over the past decade, and this study introduces an innovative Elder Fall Detection system that harnesses IoT and AI technologies. In our IoT configuration, we integrate RFID tags into smart carpets along with RFID readers to identify falls among the elderly population. To simulate fall events, we conducted experiments with 13 participants. In these experiments, RFID tags embedded in the smart carpets transmit signals to RFID readers, effectively distinguishing signals from fall events and regular movements. When a fall is detected, the system activates a green signal, triggers an alarm, and sends notifications to alert caregivers or family members. To enhance the precision of fall detection, we employed various machine and deep learning classifiers, including Random Forest (RF), XGBoost, Gated Recurrent Units (GRUs), Logistic Regression (LGR), and K-Nearest Neighbors (KNN), to analyze the collected dataset. Results show that the Random Forest algorithm achieves a 43% accuracy rate, GRUs exhibit a 44% accuracy rate, and XGBoost achieves a 33% accuracy rate. Remarkably, KNN outperforms the others with an exceptional accuracy rate of 99%. This research aims to propose an efficient fall detection framework that significantly contributes to enhancing the safety and overall well-being of independently living elderly individuals. It aligns with the principles of sustainability in IoT and AI applications.