Several theories of particle physics beyond the Standard Model consider that neutrinos can decay. In this work we assume that the standard mechanism of neutrino oscillations is altered by the decay of the heaviest neutrino mass state into a sterile neutrino and, depending on the model, a scalar or a Majoron. We study the sensitivity of the forthcoming KM3NeT-ORCA experiment to this scenario and find that it could improve the current bounds coming from oscillation experiments, where three-neutrino oscillations have been considered, by roughly two orders of magnitude. We also study how the presence of this neutrino decay can affect the determination of the atmospheric oscillation parameters sin 2 θ 23 and ∆m 2 31 , as well as the sensitivity to the neutrino mass ordering.the CP phase δ. These parameters have been measured in solar, reactor, atmospheric and long-baseline accelerator neutrino oscillation experiments. The level of precision reached by current experiments is such that, from the global picture [1-5], neutrino oscillation physics is entering the precision era. However, there are still some unknowns to be established: 1. The true ordering of neutrino masses: we still do not know if the order of the neutrino mass spectrum is normal (NO), where m 3 is the heaviest mass state, or inverted (IO), where m 2 is the heaviest one. Recent oscillation results show a preference for NO [1, 2], although the real neutrino mass ordering is not fully determined yet [6]. 2. The octant of the atmospheric angle: the measured value of sin 2 θ 23 is close to maximal (0.5), but it can be either smaller (lower octant) or larger (upper octant). 3. The exact value of the CP phase δ: values of δ ≈ 0.5π are now highly disfavored, but still a large part of the parameter space remains allowed. At 2σ confidence level, CP might be maximally violated, but also conserved. 4. The absolute scale of neutrino masses: so far there are only upper bounds on it, coming from beta decay experiments and cosmological measurements [7]. 5. The nature of neutrinos: are they Dirac or Majorana particles? In the latter case, there are two extra CP phases to be determined, which are only accessible through neutrinoless double beta decay experiments (see e.g. [8]).The last two points can not be determined by neutrino oscillation experiments, since flavor oscillations are insensitive to the absolute neutrino masses and to the Majorana CP phases. Conversely, the three first issues are expected to be solved by the future long-baseline experiment DUNE, which will measure very well the mass ordering [9] as well as the value of the CPviolating phase and the octant of the atmospheric mixing angle [10] within the standard three-neutrino picture. The determination of the mass ordering of neutrinos is also one of the main physics goals of the future atmospheric experiment ORCA (Oscillation Research with Cosmics in the Abyss) [11], that will provide precise measurements of the atmospheric parameters too. ORCA will be basically an updated version of the ANTARES neutrino...