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The discovery of a non-zero mass for neutrinos and the hierarchy between their masses invites one to search for BSM signals related to the neutrino mass. This talk will concentrate on two scenarios: the decay of heavier states into the lighter ones and pseudo-Dirac neutrinos. Both scenarios involve slow dynamical neutrino processes; therefore, a low energy neutrino flux that propagates long distances is the best candidate to show any of those signals. As a source, we will concentrate on the neutrino flux emitted by supernovas (SN). In particular, we will analyze the measurement of SN1987A. We will also explore future sensitivity by detecting another supernova or the diffuse supernova neutrino background (DSNB). In all cases, the flux is at the MeV scale and the neutrinos propagate distances on the order of ~10kpc (~Gpc) in the case of CCSN (DSNB). As the next generation of experiments, we will concentrate on Hyper-Kamiokande and DUNE that are expected to collect hundreds of events from both fluxes. By a quantitative study of how well SN and DSNB will be measured, we will estimate their future sensitivity to the neutrino lifetime and the possibility that neutrinos are pseudo-Dirac fermions.