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The population of older adults is steadily increasing, with a strong preference for aging-in-place rather than moving to care facilities. Consequently, supporting this growing demographic has become a significant global challenge. However, facilitating successful aging-in-place is challenging, requiring consideration of multiple factors such as data privacy, health status monitoring, and living environments to improve health outcomes. In this paper, we propose an unobtrusive sensor system designed for installation in older adults' homes. Using data from the sensors, our system constructs a digital twin, a virtual representation of events and activities that occurred in the home. The system uses neural network models and decision rules to capture residents' activities and living environments. This digital twin enables continuous health monitoring by providing actionable insights into residents' well-being. Our system is designed to be low-cost and privacy-preserving, with the aim of providing green and safe monitoring for the health of older adults. We have successfully deployed our system in two homes over a time period of two months, and our findings demonstrate the feasibility and effectiveness of digital twin technology in supporting independent living for older adults. This study highlights that our system could revolutionize elder care by enabling personalized interventions, such as lifestyle adjustments, medical treatments, or modifications to the residential environment, to enhance health outcomes.