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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.