Monitoring elderly people living alone is of the utmost importance given the amount of risk they are exposed to. Being aware of the activities of the elderly person in real time could help prevent/detect dangerous event that might occur such as falling. In this paper, we propose a method for activity detection using a 2D LIght Detection and Ranging (LIDAR) and deep learning. Unlike conventional work, where an activity refers to moving from one position to another, we use the term 'activity' to refer to a set of movements including walking, standing, falling and sitting. Not only does our approach detect these activities, but it also identifies a given person from his gait, and identifies unsteady gait (i.e., when he is about to fall or feeling dizzy). Throughout our experiments, we show that the proposed approach could reach an accuracy equal to 92.3% and 91.3% in activity and unsteady gait detection, respectively. It is also capable of identifying up to 3 people's gait with an accuracy equal to 92.4% using 10 seconds of walking data.