This paper studies how emergencies and failures can be managed in cable-driven parallel robots, in particular in the case of a redundant cable-suspended robot subjected to a cable breakdown. The objective is to present and test via numerical simulation the feasibility of an emergency strategy that allows the robot platform to be dynamically recovered to a safe position. Preliminary results, based on a simplified robot with a point-mass platform suspended by 4 cables, show that the proposed strategy may be an effective way to guide the platform from an unstable pose determined by the cable failure to a new static equilibrium pose.