  Sterile neutrinos can be produced through mixing with active neutrinos in the
hot and dense core of a core-collapse supernova (SN). The standard bounds on
the active-sterile mixing ($\sin^2 \theta$) from SN arise from SN1987A
energy-loss, requiring $E_{\text{loss}}<10^{52}~{\rm erg}$. In this letter, we
discuss a novel bound on sterile neutrino parameter space arising from the
energy deposition through its decays inside the SN envelope. Using the observed
underluminous SN IIP population, this energy deposition is constrained to be
below $\sim 10^{50}~{\rm erg}$. Focusing on sterile neutrino mixing only with
the tau neutrino, for heavy sterile masses $m_s$ in the range $100$-$500$ MeV,
we find stringent constraints on $\sin^2 \theta_\tau$ reaching two orders of
magnitude lower than those from the SN1987A energy-loss argument. Similar
bounds will also be applicable to sterile mixing only with muons ($\sin^2
\theta_\mu$).
