Injection-induced aseismic slip plays an important role in a broad range of human-made and natural systems, from the exploitation of geo-resources to the understanding of earthquakes. Recent studies have shed light on how aseismic slip propagates in response to continuous fluid injections. Yet much less is known about the response of faults after the injection of fluids has stopped. In this work, we investigate via a hydro-mechanical model the propagation and ultimate arrest of aseismic slip during the so-called post-injection stage. We show that after shut-in, fault slip propagates in pulse-like mode. The conditions that control the propagation as a pulse and notably when and where the ruptures arrest are fully established. In particular, critically stressed faults can host rupture pulses that propagate for several orders of magnitude the injection duration and reach up to nearly double the size of the ruptures at the moment of shut-in. We consequently argue that the persistent stressing of increasingly larger rock volumes caused by post-injection aseismic slip is a plausible mechanism for the triggering of post-injection seismicity-a critical issue in the geo-energy industry. Our physical model shows quantitative agreement with field observations of documented cases of post-injection induced seismicity.