  In this paper, we study the role of the symmetry energy on the neutron-drip
transition in both nonaccreting and accreting neutron stars, allowing for the
presence of a strong magnetic field as in magnetars. The density, pressure, and
composition at the neutron-drip threshold are determined using the recent set
of the Brussels-Montreal microscopic nuclear mass models, which mainly differ
in their predictions for the value of the symmetry energy $J$ and its slope $L$
in infinite homogeneous nuclear matter at saturation. Although some
correlations between on the one hand the neutron-drip density, the pressure,
the proton fraction and on the other hand $J$ (or equivalently $L$) are found,
these correlations are radically different in nonaccreting and accreting
neutron stars. In particular, the neutron-drip density is found to increase
with $L$ in the former case, but decreases in the latter case depending on the
composition of ashes from x-ray bursts and superbursts. We have qualitatively
explained these different behaviors using a simple mass formula. We have also
shown that the details of the nuclear structure may play a more important role
than the symmetry energy in accreting neutron-star crusts.
