  Neutrinoless double beta decay ($\beta\beta0\nu$) is among the only realistic
probes of Majorana neutrinos. In the standard scenario, dominated by light
neutrino exchange, the process amplitude is proportional to $m_{ee}$, the $e-e$
element of the Majorana mass matrix. Naively, current data allows for vanishing
$m_{ee}$, but this should be protected by an appropriate flavor symmetry. All
such symmetries lead to mass matrices inconsistent with oscillation
phenomenology. I perform a spurion analysis to break all possible Abelian
symmetries that guarantee vanishing $\beta\beta0\nu$ rates and search for
minimally allowed values. I survey 230 broken structures to yield $m_{ee}$
values and current phenomenological constraints under a variety of scenarios.
This analysis also extracts predictions for both neutrino oscillation
parameters and kinematic quantities. Assuming reasonable tuning levels, I find
that $m_{ee}>4\times 10^{-6}$ eV at 99% confidence. Bounds below this value
might indicate the Dirac neutrino nature or the existence of new light (eV-MeV
scale) degrees of freedom that can potentially be probed elsewhere.
