  The invisible decay of cold dark matter into a slightly lighter dark sector
particle on cosmological time-scales has been proposed as a solution to the
$S_8$ tension. In this work we discuss the possible embedding of this scenario
within a particle physics framework, and we investigate its phenomenology. We
identify a minimal dark matter decay setup that addresses the $S_8$ tension,
while avoiding the stringent constraints from indirect dark matter searches. In
our scenario, the dark sector contains two singlet fermions $N_{1,2}$,
quasi-degenerate in mass, and carrying lepton number so that the heaviest state
($N_2$) decays into the lightest ($N_1$) and two neutrinos via a
higher-dimensional operator $N_2\to \bar N_1\nu\nu$. The conservation of lepton
number, and the small phase-space available for the decay, forbids the decay
channels into hadrons and strongly suppresses the decays into photons or
charged leptons. We derive complementary constraints on the model parameters
from neutrino detectors, freeze-in dark matter production via $\nu\nu\to
N_1N_2$, collider experiments and blazar observations, and we show that the
upcoming JUNO neutrino observatory could detect signals of dark matter decay
for model parameters addressing the $S_8$ tension if the dark matter mass is
below $\simeq 1$ GeV.
