  The search for a dark photon produced at $e^{+}e^{-}$ colliders which
subsequently decays into inelastic dark matter particles, is discussed. The
heavier dark matter decays into a pair of visible charged particles and a
lighter dark matter particle after traveling some distance. The visible decay
products can be recorded by a dark matter detector made of emulsions and gas
detectors, placed near the main $e^{+}e^{-}$ detector. This setup can not only
explore new parameter regions not reached before, but also re-open some regions
thought to be excluded by previous experimental data. The physics potential for
such a detector around BESIII and Belle II is presented.
