  We study the dynamics of a one-dimensional Bose gas in presence of strong
two-body losses. In this dissipative quantum Zeno regime, the gas fermionises
and its dynamics can be described with a simple set of rate equations.
Employing the local density approximation and a Boltzmann-like dynamical
equation, the description is easily extended to take into account an external
potential. We show that in the absence of confinement the population is
depleted in an anomalous way and that the gas behaves as a low-temperature
classical gas. The harmonic confinement accelerates the depopulation of the gas
and introduces a novel decay regime, which we thoroughly characterise.
