  The KOTO experiment has reported an excess of $K_L\to\pi^0\nu\bar\nu$ events
above the Standard Model prediction, in tension with the Grossman-Nir (GN)
bound. The GN bound heavily constrains new physics interpretations of an excess
in this channel, but another possibility is that the observed events originate
from a different process entirely: a decay of the form $K_L\to\pi^0X$, where
$X$ denotes one or more new invisible species. We introduce a class of models
to study this scenario with two light scalars playing the role of $X$, and we
examine the possibility that the lighter of the two new states may also account
for cosmological dark matter (DM). We show that this species can be produced
thermally in the presence of additional interactions apart from those needed to
account for the KOTO excess. Conversely, in the minimal version of the model,
DM must be produced nonthermally. In this case, avoiding overproduction imposes
constraints on the structure of the low-energy theory. Moreover, this
requirement carries significant implications for the scale of reheating in the
early Universe, generically preferring a low but observationally permitted
reheating temperature of O(10 MeV). We discuss astrophysical and terrestrial
signatures that will allow further tests of this paradigm in the coming years.
