  We investigate the entanglement dynamics in a free-fermion chain initially
prepared in a Fermi sea and subjected to localized losses (dissipative
impurity). We derive a formula describing the dynamics of the entanglement
entropies in the hydrodynamic limit of long times and large intervals. The
result depends only on the absorption coefficient of the effective delta
potential describing the impurity in the hydrodynamic limit. Genuine
dissipation-induced entanglement is certified by the linear growth of the
logarithmic negativity. Finally, in the quantum Zeno regime at strong
dissipation the entanglement growth is arrested (Zeno entanglement death).
