  Symmetry protected topological (SPT) phases are gapped quantum phases which
host symmetry-protected gapless edge excitations. On the other hand, the edge
states can be gapped by spontaneously breaking symmetry. We show that
topological defects on the symmetry-broken edge cannot proliferate due to their
fractional statistics. A gapped symmetric boundary, however, can be achieved
between an SPT phase and certain fractionalized phases by condensing the bound
state of a topological defect and an anyon. We demonstrate this by two examples
in two dimensions: an exactly solvable model for the boundary between
topological Ising paramagnet and double semion model, and a fermionic example
about the quantum spin Hall edge. Such a hybrid structure containing both SPT
phase and fractionalized phase generally support ground state degeneracy on
torus.
