  The presence of a planetary system can shield a planetesimal disk from the
secular gravitational perturbations due to distant outer massive objects
(planets or stellar companions). As the host star evolves off the main sequence
to become a white dwarf, these planets can be engulfed, triggering secular
instabilities and leading to the tidal disruptions of small rocky bodies. These
disrupted bodies can feed the white dwarfs with rocky material and possibly
explain the high-metallicity material in their atmospheres. We illustrate how
this mechanism can operate when the gravitational perturbations are due to the
Kozai-Lidov mechanism from a stellar binary companion. We show that this
mechanism can explain the observed levels of accretion if: (1) the planetary
engulfment happens fast compared to the secular timescale, which is generally
the case for wide binaries ($>100$ AU) and planetary engulfment during the
Asymptotic Giant Branch; (2) the planetesimal disk has a total mass of
$\sim10^{-4}-10^{-2}M_\oplus$. We show that this new mechanism can provide a
steady supply of material throughout the entire life of the white dwarfs for
all cooling ages and can account for a large fraction (up to nearly half) of
the observed polluted WDs.
