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We consider the class of models where Dirac neutrino masses at one loop andthe dark matter stability can be obtained using only the global $U(1)_{B-L}$symmetry already present in Standard Model. We discuss how the residual$\mathcal{Z}_n$ subgroup, left unbroken after the breaking of $U(1)_{B-L}$,dictates the neutrino nature, namely if they are Dirac or Majorana particles,as well as determines the stability of the dark matter candidate in suchmodels. In particular, we show that without the correct breaking of$U(1)_{B-L}$ to an appropriate residual $\mathcal{Z}_n$ symmetry, the Diracnature of neutrinos and/or dark matter stability might be lost. Forcompleteness we also provide some examples where the dark matter stability isaccidental or lost completely. Finally, we discuss one example model where theDirac neutrinos with naturally small one loop masses as well as dark matterstability, are both protected by the same residual $\mathcal{Z}_6$ subgroup,without need for adding any new explicit or accidental symmetries beyond theStandard Model symmetries.

The role of residual symmetries in dark matter stability and the neutrino nature