  In the beyond Standard Model (BSM) scenarios, the possibility of neutrinos
decaying into a lighter state is one of the prime quests for the new-generation
neutrino experiments. The observation of high-energy astrophysical neutrinos by
IceCube opens up a new avenue for studying neutrino decay. In this work, we
investigate a novel scenario of invisible neutrino decay to axionlike particles
(ALPs). These ALPs propagate unattenuated and reconvert into gamma rays in the
magnetic field of the Milky Way. This is complementary and independent of the
previously done studies where gamma rays produced at the source are used to
investigate the ALP hypothesis. We exploit the Fermi-LAT and IceCube
observations of NGC 1068 to set constraints on the ALP parameters. Being a
steady source of neutrinos, it offers a better prospect over transient sources.
We obtain 95% confidence level (CL) upper limits on the photon-ALP coupling
constant $g_{a\gamma}\lesssim 1.37 \times 10^{-11}$ GeV$^{-1}$ for ALP masses
$m_{a} \leq 2 \times 10^{-9}$ eV. Our results are comparable to previous upper
limits obtained using the GeV to sub-PeV gamma-ray observations. Moreover, we
estimate the contribution from NGC 1068-like sources to diffuse gamma-ray flux
at GeV energies under the ALP scenario.
