  We explore spherically symmetric stationary solutions, generated by ``stars''
with regular interiors, in purely massive gravity. We reexamine the claim that
the resummation of non-linear effects can cure, in a domain near the source,
the discontinuity exhibited by the linearized theory as the mass m of the
graviton tends to zero. First, we find analytical difficulties with this claim,
which appears not to be robust under slight changes in the form of the mass
term. Second, by numerically exploring the inward continuation of the class of
asymptotically flat solutions, we find that, when m is ``small'', they all end
up in a singularity at a finite radius, well outside the source, instead of
joining some conjectured ``continuous'' solution near the source. We reopen,
however, the possibility of reconciling massive gravity with phenomenology by
exhibiting a special class of solutions, with ``spontaneous symmetry breaking''
features, which are close, near the source, to general relativistic solutions
and asymptote, for large radii, a de Sitter solution of curvature ~m^2.
