  Common-envelope evolution - where a star is engulfed by a companion - is a
critical but poorly understood step in, e.g., the formation pathways for
gravitational-wave sources. However, it has been extremely challenging to
identify observable signatures of such systems. We show that for systems
involving a neutron star, the hypothesized super-Eddington accretion onto the
neutron star produces MeV-range, months-long neutrino signals within reach of
present and planned detectors. While there are substantial uncertainties on the
rate of such events (0.01-1/century in the Milky Way) and the neutrino
luminosity (which may be less than the accretion power), this signal can only
be found if dedicated new searches are developed. If detected, the neutrino
signal would lead to significant new insights into the astrophysics of
common-envelope evolution.
