  Light hypothetical particles with masses up to $\mathcal{O}(100)\ {\rm MeV}$
can be produced in the core of supernovae. Their subsequent decays to neutrinos
can produce a flux component with higher energies than the standard flux. We
study the impact of heavy neutral leptons, $Z'$ bosons, in particular ${\rm
U(1)}_{L_\mu-L_\tau}$ and ${\rm U(1)}_{B-L}$ gauge bosons, and majorons coupled
to neutrinos flavor-dependently. We obtain new strong limits on these particles
from no events of high-energy SN 1987A neutrinos and their future sensitivities
from observations of galactic supernova neutrinos.
