  We study the hydrodynamic limit for a periodic $1$-dimensional exclusion
process with a dynamical constraint, which prevents a particle at site $x$ from
jumping to site $x\pm1$ unless site $x\mp1$ is occupied. This process with
degenerate jump rates admits transient states, which it eventually leaves to
reach an ergodic component, assuming that the initial macroscopic density is
larger than $\frac{1}{2}$, or one of its absorbing states if this is not the
case. It belongs to the class of conserved lattice gases (CLG) which have been
introduced in the physics literature as systems with active-absorbing phase
transition in the presence of a conserved field. We show that, for initial
profiles smooth enough and uniformly larger than the critical density
$\frac{1}{2}$, the macroscopic density profile for our dynamics evolves under
the diffusive time scaling according to a fast diffusion equation (FDE). The
first step in the proof is to show that the system typically reaches an ergodic
component in subdiffusive time.
