One of the major healthcare challenges is elderly fallers. A fall can lead to disabilities and even mortality. With the current Covid-19 pandemic, insufficient resources could be provided for the care of elderlies, and care workers often may not be able to visit them. Therefore, a fall may get undetected or delayed leading to serious harm or consequences. Automatic fall detection systems could provide the necessary detection and warnings for timely intervention. Although many sensor-based fall detection systems have been proposed, most systems focus on the sudden fall and have not considered the slow fall scenario, a typical fall instance for elderly fallers. In this paper, a robust activity (RA) and slow fall detection system is proposed. The system consists of a waist-worn wearable sensor embedded with an inertial measurement unit (IMU) and a barometer, and a reference ambient barometer. A deep neural network (DNN) is developed for fusing the sensor data and classifying fall events. The results have shown that the IMU-barometer design yield better detection of fall events and the DNN approach (90.33% accuracy) outperforms traditional machine learning algorithms.