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Whether the neutrino mass ordering is normal or inverted remains an experimentally open issue in neutrino physics. The knowledge of neutrino mass ordering has great importance for neutrinoless double-beta ($ 0\nu\beta\beta$) decay experiments, which can establish the nature of massive neutrinos, i.e., whether they are Dirac or Majorana fermions. Recently, the KamLAND-Zen 800 measurement has reached for the first time the parameter space of the inverted ordering with a vanishing lightest neutrino mass. By assuming the inverted ordering, we attempt to derive the physical information of the neutrino nature and Majorana CP phases from a negative or positive observation of $ 0\nu\beta\beta$ decays in the near future. Moreover, the possibility of extracting the nuclear matrix element in the case of a positive observation is also examined. To avoid the ambiguity from unknown priors of neutrino masses, we adopt the maximum likelihood method instead of the Bayesian approach usually considered in previous works., Comment: 13 pages, 7 figures, version published in EPJC