  We explore the possibility that the dark matter relic density is not produced
by thermal mechanism directly, but by the decay of other heavier dark sector
particles which on the other hand can be produced by the thermal freeze-out
mechanism. Using a concrete model with a light dark matter from dark sector
decay, we study the collider signature of the dark sector particles in
association with Higgs production processes. We find that the future lepton
colliders can be a better place to probe the signature of this kind of light
dark matter model than the hadron collider such as LHC. Meanwhile, it is found
that a Higgs factory with center of mass energy 250 GeV has a better potential
to resolve the signature of this kind of light dark matter model than the Higgs
factory with center of mass energy 350 GeV.
