Robots were placed under fixed safeguards in the early stages of robotics development. Safety and real-time risk assessment are not easy, especially when robots are in places that co-exist with humans. However, robot and human interaction have essential applications in human physical assistance, human-robot task coordination and cooperation. This paper presents our proposed new approach to developing shared autonomy under safety. We derive the shared autonomy policies and explain how safety is quantified. After demonstrating an experiment result, the paper describes open problems that will be investigated in future research activities. It also covers how it can have potential applications in industry, welfare, and rescue.