Highly automated road vehicles need the capability of stopping safely in a situation that disrupts continued normal operation, e.g. due to internal system faults. Motion planning for safe stop differs from nominal motion planning, since there is not a specific goal location. Rather, the desired behavior is that the vehicle should reach a stopped state, preferably outside of active lanes. Also, the functionality to stop safely needs to be of high integrity. The first contribution of this paper is to formulate the safe stop problem as a benchmark optimal control problem, which can be solved by dynamic programming. However, this solution method cannot be used in real-time. The second contribution is to develop a real-time safe stop trajectory planning algorithm, based on selection from a precomputed set of trajectories. By exploiting the particular properties of the safe stop problem, the cardinality of the set is decreased, making the algorithm computationally efficient. Furthermore, a monitoring based architecture concept is proposed, that ensures dependability of the safe stop function. Finally, a proof of concept simulation using the proposed architecture and the safe stop trajectory planner is presented.