We demonstrate that field theories involving explicit breaking of cont
inous symmetries incorporate two generic classes of topological defect
s each of which is stable for a particular range of parameters. The fi
rst class includes defects of the usual type where the symmetry gets r
estored in the core and vacuum energy gets trapped there. We show, how
ever, that these defect solutions become unstable for certain ranges o
f parameters and decay not to the vacuum but to another type of stable
defect where the symmetry in not restored in the core. In the wall ca
se, initially spherical, bubblelike configurations are simulated numer
ically and shown to evolve generically towards a planar collapse. In t
he string case, the decay of the symmetric core vortex resembles the d
ecay of a semilocal string to a Skyrmion with the important difference
that while the Skyrmion is unstable and decays to the vacuum, the res
ulting nonsymmetric vortex is topologically stable.