  In insulating crystals, it was previously shown that defects with two fewer
dimensions than the bulk can bind topological electronic states. We here
further extend the classification of topological defect states by demonstrating
that the corners of crystalline defects with integer Burgers vectors can bind
0D higher-order end (HEND) states with anomalous charge and spin. We
demonstrate that HEND states are intrinsic topological consequences of the bulk
electronic structure and introduce new bulk topological invariants that are
predictive of HEND dislocation states in solid-state materials. We demonstrate
the presence of first-order 0D defect states in PbTe monolayers and HEND states
in 3D SnTe crystals. We relate our analysis to magnetic flux insertion in
insulating crystals. We find that $\pi$-flux tubes in inversion- and
time-reversal-symmetric (helical) higher-order topological insulators bind
Kramers pairs of spin-charge-separated HEND states, which represent observable
signatures of anomalous surface half quantum spin Hall states.
