  We introduce leak-in dark matter, a novel out-of-equilibrium origin for the
dark matter (DM) in the universe. We provide a comprehensive and unified
discussion of a minimal, internally-thermalized, hidden sector populated from
an out-of-equilibrium, feeble connection to the hotter standard model (SM)
sector. We emphasize that when this out-of-equilibrium interaction is
renormalizable, the colder sector undergoes an extended phase of non-adiabatic
evolution largely independent of initial conditions, which we dub "leak-in." We
discuss the leak-in phase in generality, and establish the general properties
of dark matter that freezes out from a radiation bath undergoing such a leak-in
phase. As a concrete example, we consider a model where the SM has an
out-of-equilibrium B-L vector portal interaction with a minimal hidden sector.
We discuss the interplay between leak-in and freezein processes in this theory
in detail and demonstrate regions where leak-in yields the full relic
abundance. We study observational prospects for B-L vector portal leak-in DM,
and find that despite the requisite small coupling to the SM, a variety of
experiments can serve as sensitive probes of leak-in dark matter. Additionally,
regions allowed by all current constraints yield DM with self-interactions
large enough to address small-scale structure anomalies.
