  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 an 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. We discuss evidence that supports
this mechanism based on documented cases of post-injection-induced seismicity.
