  In a simple framework which naturally incorporates dark matter stability and
neutrino phenomenology, we compute all the possible texture zeros which arise
when the non-abelian flavor symmetry A4 is spontaneously broken to Z2. As a
result, we obtain four textures with two vanishing matrix elements. Two of such
textures predict a zero contribution to the neutrinoless double beta decay
effective mass parameter at tree level, and as a one loop bound we get
$m_{ee}<8\times 10^{-2}$ meV. These are compatible with the normal ordering for
the neutrino masses and the allowed range for the lightest neutrino mass is
between $m_{\nu_{min}}\sim3$ meV and $m_{\nu_{max}}\sim8$ meV. Additionally we
obtain dark matter stability linked to the way the flavor symmetry is broken,
leaving a residual Z2 symmetry
