  We theoretically investigate the fate of a neutron-alpha $p$-wave resonance
in dilute neutron matter, which may be encountered in neutron stars and
supernova explosions. While $^5$He is known as a resonant state that decays to
a neutron and an alpha particle in vacuum, this unstable state turns into a
stable bound state in the neutron Fermi sea because the decay process is
forbidden by the Pauli-blocking effect of neutrons. Such a resonance-to-bound
transition assisted by the Pauli-blocking effect can be realized in cold atomic
experiments for a quantum mixture near the heteronuclear Feshbach resonance.
