  In recent years, controlled dissipation has proven to be a useful tool for
probing of a quantum system in the ultracold setup. In this paper we consider
dynamics of bosons induced by a dissipative local defect. We address superfluid
and supersolid phases close to half-filling that are ground states of an
extended Bose-Hubbard Hamiltonian. To this end, we solve the master equation
using the Gutzwiller approximation and find that in the superfluid phase
repulsive nearest neighbour interactions can lead to enhanced dissipation
processes. On the other hand, our mean-field approach indicates that the
effective loss rates are significantly suppressed deep in the supersolid phase
where repulsive nearest neighbour interactions play a dominant role. Our
numerical results are explained by analytical arguments and in particular, in
the limit of strong dissipation we recover the quantum Zeno effect.
