  The standard expectation is that gauge fixing cannot alter the physics in the
physical sector of a Yang-Mills theory. Here we argue that this may not always
be true: in an SU(2) Yang-Mills theory in which the $SU(2)/U(1)$ coset is
non-perturbatively gauge fixed, we find that a new phase, with spontaneous
symmetry breaking and a Higgs-like mechanism, appears to be a possibility.
