  The large distances travelled by neutrinos emitted from the Sun and
core-collapse supernovae together with the characteristic energy of such
neutrinos provide ideal conditions to probe their lifetime, when the decay
products evade detection. We investigate the prospects of probing invisible
neutrino decay capitalising on the detection of solar and supernova neutrinos
as well as the diffuse supernova neutrino background (DSNB) in the
next-generation neutrino observatories Hyper-Kamiokande, DUNE, JUNO, DARWIN,
and RES-NOVA. We find that future solar neutrino data will be sensitive to
values of the lifetime-to-mass ratio $\tau_1/m_1$ and $\tau_2/m_2$ of
$\mathcal{O}(10^{-1} - 10^{-2})$ s/eV. From a core-collapse supernova explosion
at $10$ kpc, lifetime-to-mass ratios of the three mass eigenstates of
$\mathcal{O}(10^5)$ s/eV could be tested. After $20$ years of data taking, the
DSNB would extend the sensitivity reach of $\tau_1/m_1$ to $10^{8}$ s/eV. These
results promise an improvement of about $6 -15$ orders of magnitude on the
values of the decay parameters with respect to existing limits.
