In this paper, we present an improved collision avoidance algorithm conceived to deal with zero-speed pedestrians in a crowd. A zero-speed pedestrian is a pedestrian who stops for a short, undefined period to rest, use a phone, or communicate with others, and then resumes walking later. Zero-speed pedestrians can be encountered in places such as shopping centers, sidewalks with retail stores, or public gatherings. When integrated into a crowd simulation, zero-speed pedestrians can cause blockages, particularly livelocks, as observed when using the Optimal Reciprocal Collision Avoidance (ORCA) algorithm. A livelock in a simulation is a situation where an agent is blocked but still has room to move. If the livelock is not handled properly, it will invalidate the simulation runs. We provide insight into the causes of livelocks and propose a modification of ORCA that successfully prevents livelocks from occurring in typical situations in which they can be observed using ORCA. Among other applications, this model can be used as a crowd management tool to evaluate the impact of zero-speed pedestrians on crowd flow.