  We consider the Bose-Hubbard model with particle losses at one lattice site.
For the non-interacting case, we find that half of the bosons of an initially
homogeneous particle distribution, are not affected by dissipation that only
acts on one lattice site in the center of the lattice. A physical
interpretation of this result is that the surviving particles interfere
destructively when they tunnel to the location of the dissipative defect and
therefore never reach it. Furthermore we find for a one-dimensional model that
a fraction of the particles can propagate across the dissipative defect even if
the rate of tunneling between adjacent lattice sites is much slower than the
loss rate at the defect. In the interacting case, the phase coherence is
destroyed and all particles eventually decay. We thus analyze the effect of
small interactions and small deviations from the perfectly symmetric setting on
the protection of the particles against the localized losses. A possible
experimental realization of our setup is provided by ultracold bosonic atoms in
an optical lattice, where an electron beam on a single lattice site ionizes
atoms that are then extracted by an electrostatic field.
