  A model of compact object coupled to inhomogeneous anisotropic dark energy is
studied. It is assumed a variable dark energy that suffers a phase transition
at a critical density. The anisotropic Lambda-Tolman-Oppenheimer-Volkoff
equations are integrated to know the structure of these objects. The anisotropy
is concentrated on a thin shell where the phase transition takes place, while
the rest of the star remains isotropic. The family of solutions obtained
depends on the coupling parameter between the dark energy and the fermion
matter. The solutions share several features in common with the gravastar
model. There is a critical coupling parameter that gives non-singular black
hole solutions. The mass-radius relations are studied as well as the internal
structure of the compact objects. The hydrodynamic stability of the models is
analyzed using a standard test from the mass-radius relation. For each
permissible value of the coupling parameter there is a maximum mass, so the
existence of black holes is unavoidable within this model.
