In general, we study dark matter production via freeze-out or freeze-in, for instance. The former produces thermal dark matter particles which correspond to a class of particle called Weakly Interacting Massive Particles (WIMPs). The later is related to non-thermal dark matter production, corresponding to Feebly Interacting Massive Particles (FIMPs). That's what one quickly finds in the literature.
My question instead goals to know whether is possible FIMPs (WIMPs) be (non-)thermally produced via freeze-out(-in) or not, and why.