To develop socially assistive robots for monitoring older adults at home, a sensor is required to identify residents and capture activities within the room without violating privacy. We focused on 2D Light Detection and Ranging (2D-LIDAR) capable of robustly measuring human contours in a room. While horizontal 2D contour data can provide human location, identifying humans and activities from these contours is challenging. To address this issue, we developed novel methods using deep learning techniques. This paper proposes methods for person identification and activity estimation in a room using contour point clouds captured by a single 2D-LIDAR at hip height. In this approach, human contours were extracted from 2D-LIDAR data using density-based spatial clustering of applications with noise. Subsequently, the person and activity within a 10-s interval were estimated employing deep learning techniques. Two deep learning models, namely Long Short-Term Memory (LSTM) and image classification (VGG16), were compared. In the experiment, a total of 120 min of walking data and 100 min of additional activities (door opening, sitting, and standing) were collected from four participants. The LSTM-based and VGG16-based methods achieved accuracies of 65.3% and 89.7%, respectively, for person identification among the four individuals. Furthermore, these methods demonstrated accuracies of 94.2% and 97.9%, respectively, for the estimation of the four activities. Despite the 2D-LIDAR point clouds at hip height containing small features related to gait, the results indicate that the VGG16-based method has the capability to identify individuals and accurately estimate their activities.