This paper addresses the problem of navigating a mobile robot with a limited field-of-view in a unknown dynamic environment. In such a situation, absolute motion safety, i.e. such that no collision will ever take place whatever happens, is impossible to guarantee. It is therefore settled for a weaker level of motion safety dubbed passive motion safety: it guarantees that, if a collision takes place, the robot will be at rest. Passive motion safety is tackled using a variant of the Inevitable Collision State (ICS) concept called Braking ICS, i.e. states such that, whatever the future braking trajectory of the robot, a collision occurs before it is at rest. Passive motion safety is readily obtained by avoiding Braking ICS at all times. Building upon an existing Braking ICS-Checker, i.e. an algorithm that checks if a given state is a Braking ICS or not, this paper presents a reactive collision avoidance scheme called PassAvoid. The main contribution of this paper is the formal proof of PassAvoid's passive motion safety. Experiments in simulation demonstrates how PassAvoid operates.