  We study the asymptotic behaviour of the symmetric zero-range process in the
finite lattice $\{1,\ldots, N-1\}$ with slow boundary, in which particles are
created at site $1$ or annihilated at site $N\!-\!1$ with a rate proportional
to $N^{-\theta}$, for $\theta\geq 1$. We present the invariant measure for this
model and obtain the hydrostatic limit. In order to understand the asymptotic
behaviour of the spatial-temporal evolution of this model under the diffusive
scaling, we start to analyze the hydrodynamic limit, exploiting attractiveness
as an essential ingredient. We obtain that the hydrodynamic equation has
boundary conditions that depend on the value of $\theta$.
