  Heavy sterile neutrinos with masses ${\mathcal O}(100)$ MeV mixing with
active neutrinos can be produced in the core of a collapsing supernova (SN). In
order to avoid an excessive energy loss, shortening the observed duration of
the SN 1987A neutrino burst, we show that the active-sterile neutrino mixing
angle should satisfy $\sin^2 \theta \lesssim 5 \times 10^{-7}$. For a mixing
with tau flavour, this bound is much stronger than the ones from laboratory
searches. Moreover, we show that in the viable parameter space the decay of
such "heavy" sterile neutrinos in the SN envelope would lead to a very
energetic flux of daughter active neutrinos; if not too far below current
limits, this would be detectable in large underground neutrino observatories,
like Super-Kamiokande, as a (slightly time-delayed) high-energy bump in the
spectrum of a forthcoming Galactic SN event.
