  The propagation of damage on the square Ising lattice with a corner geometry
is studied by means of Monte Carlo simulations. It is found that, just at
$T=T_f (h)$ (critical temperature of the filling transition) the damage
initially propagates along the interface of the competing domains, according to
a power law given by $D(t) \propto t^{\eta}$. The value obtained for the
dynamic exponent ($\eta^{*} = 0.89(1)$) is in agreement with that corresponding
to the wetting transition in the slit geometry (Abraham Model) given by
$\eta^{WT} = 0.91(1)$. However, for later times the propagation crosses to a
new regime such as $\eta^{**} = 0.40 \pm 0.02$, which is due to the propagation
of the damage into the bulk of the magnetic domains. This result can be
understood due to the constraints imposed to the propagation of damage by the
corner geometry of the system that cause healing at the corners where the
interface is attached.
