  We study the $\mathbb{Z}_2$ Bose-Hubbard model at incommensurate densities,
which describes a one-dimensional system of interacting bosons whose tunneling
is dressed by a dynamical $\mathbb{Z}_2$ field. At commensurate densities, the
model is known to host intertwined topological phases, where long-range order
coexists with non-trivial topological properties. This interplay between
spontaneous symmetry breaking (SSB) and topological symmetry protection gives
rise to interesting fractional topological phenomena when the system is doped
to certain incommensurate fillings. In particular, we hereby show how
topological defects in the $\mathbb{Z}_2$ field can appear in the ground state,
connecting different SSB sectors. These defects are dynamical and can travel
through the lattice carrying both a topological charge and a fractional
particle number. In the hardcore limit, this phenomenon can be understood
through a bulk-defect correspondence. Using a pumping argument, we show that it
survives also for finite interactions, demonstrating how boson
fractionalization can occur in strongly-correlated bosonic systems, the main
ingredients of which have already been realized in cold-atom experiments.
