Most injuries in the elderly are due to falls. The response time, to attend to the critically injured in such fall cases, is crucial to their survival. This paper presents a low-cost, autonomous assistive patrol robot which additionally includes a fallen person detection module with facial recognition that allows identification of patients. Patrol robots could be beneficial for care centers, where there is a considerable number of patients that require care. In these conditions, falls can be generally detected by the robotic platform during the post-fall phase. This allows the system to work with no frame rate constraints, allowing other tasks to be run simultaneously. Based on the YOLO network, we propose two approaches for the fallen person detector. The first approach can differentiate between fallen persons and persons doing ordinary activity in a single stage, while the second is a two-staged approach. The network weights were obtained using a fine-tuning process by retraining with our own extended Fall Person Dataset (E-FPDS), which we release as a benchmark for other RGB vision-based approaches. Quantitative evaluations confirm that the detector performs robustly in detecting fallen persons in different situations. The results also show a recall of 98.97% in our test set.