  There are many extensions of the Standard Model with a dark matter (DM)
candidate obtained via the freeze-out mechanism. It can happen that after all
experimental and theoretical constraints are taken into account, all parameter
points have a relic density below the experimentally measured value. This means
that the models solve only partially the DM problem, and at least one more
candidate is needed. In this work we show that it is possible to further extend
the model with a DM candidate obtained via the freeze-in mechanism to be in
agreement with the relic density experimental measurement. Once the relic
density problem is solved with this addition, new questions are raised. This
new model with at least two DM candidates could have a freeze-out undetectable
DM particle both in direct and indirect detection. This could happen if the
freeze-out DM particle would have a very low density. Hence, a collider DM hint
via excess in the missing energy with no correspondence in direct and indirect
detection experiments, could signal the existence of a Feebly Interacting
Massive Particle (FIMP). Conversely, if a DM particle is found and a particular
model can explain all observables except the correct relic density, an
extension with an extra FIMP would solve the problem. The freeze-in DM
candidate, due to the small portal couplings, will not change the remaining
phenomenology.
