  The neutrinoless double beta decay experimental effort continues to make
tremendous progress with hopes of covering the inverted neutrino mass hierarchy
in coming years and pushing from the quasi-degenerate hierarchy into the normal
hierarchy. As neutrino oscillation data is starting to suggest that the mass
ordering may be normal, we may well be faced with staring down the funnel of
death: a region of parameter space in the normal ordering where -- for a
particular cancellation among the absolute neutrino mass scale, the Majorana
phases, and the oscillation parameters -- the neutrinoless double beta decay
rate may be vanishingly small. To answer the question of whether this region of
parameter space is theoretically preferred, we survey five broad categories of
flavor model structures which make various different predictions for parameters
relevant for neutrinoless double beta decay to determine how likely it is that
the rate may be in this funnel region. We find that a non-negligible fraction
of predictions surveyed are at least partially in the funnel region. Our
results can guide model builders and experimentalists alike in focusing their
efforts on theoretically motivated regions of parameter space.
