  We experimentally investigate the action of a localized dissipative potential
on a macroscopic matter wave, which we implement by shining an electron beam on
an atomic Bose-Einstein condensate (BEC). We measure the losses induced by the
dissipative potential as a function of the dissipation strength observing a
paradoxical behavior when the strength of the dissipation exceeds a critical
limit: for an increase of the dissipation rate the number of atoms lost from
the BEC becomes lower. We repeat the experiment for different parameters of the
electron beam and we compare our results with a simple theoretical model,
finding excellent agreement. By monitoring the dynamics induced by the
dissipative defect we identify the mechanisms which are responsible for the
observed paradoxical behavior. We finally demonstrate the link between our
dissipative dynamics and the measurement of the density distribution of the BEC
allowing for a generalized definition of the Zeno effect. Due to the high
degree of control on every parameter, our system is a promising candidate for
the engineering of fully governable open quantum systems.
