  Tensions in the measurements of neutron and kaon weak decays, such as of the
neutron lifetime, may speak to the existence of new particles and dynamics not
present in the Standard Model (SM). In scenarios with dark sectors, particles
that couple feebly to those of the SM appear. We offer a focused overview of
such possibilities and describe how the observations of neutron stars, which
probe either their structure or dynamics, limit them. In realizing these
constraints, we highlight how the assessment of particle processes within dense
baryonic matter impacts the emerging picture -- and we emphasize both the
flavor structure of the constraints and their broader connections to cogenesis
models of dark matter and baryogenesis.
