Autonomous rendezvous, proximity operations, and docking are key enablers of missions such as satellite servicing, active debris removal, and in-space assembly. However, errors in the control and estimation systems, or failures to account for off-nominal conditions may result in catastrophic collisions between spacecraft. Safety may potentially be preserved in these cases by switching to a safety-driven backup system. This paper develops such a system, with guidance, control, and estimation schemes designed to safely place an active chaser spacecraft in a parking orbit around a passive target spacecraft. Natural motion trajectories are considered to identify a set of passively safe parking orbits under Clohessy-Wiltshire-Hill dynamics, and a mixed integer programming formulation is developed to find the optimal transfer trajectories to this set. The practicality of the estimation and control schemes is demonstrated though simulated case studies. The guidance algorithm is integrated into a run time assurance framework, which allows real-time enforcement of the safety constraints in a least-intrusive fashion.