  Accidental matter models are scenarios where the beyond-the-standard model
physics preserves all the standard model accidental and approximate symmetries
up to a cutoff scale related with lepton number violation. We study such
scenarios assuming that the new physics plays an active role in neutrino mass
generation, and show that this unavoidably leads to radiatively induced
neutrino masses. We systematically classify all possible models and determine
their viability by studying electroweak precision data, big bang
nucleosynthesis and electroweak perturbativity, finding that the latter places
the most stringent constraints on the mass spectra. These results allow the
identification of minimal radiative accidental matter models for which
perturbativity is lost at high scales. We calculate radiative charged-lepton
flavor violating processes in these setups, and show that $\mu\to e \gamma$ has
a rate well within MEG sensitivity provided the lepton-number violating scale
is at or below $10^6$ GeV, a value (naturally) assured by the radiative
suppression mechanism. Sizeable $\tau\to \mu \gamma$ branching fractions within
SuperKEKB sensitivity are possible for lower lepton-number breaking scales. We
thus point out that these scenarios can be tested not only in direct searches
but also in lepton-flavor violating experiments.
