  In two-dimensional topological insulators, a disorder induced topological
phase transition is typically identified with an Anderson localization
transition at the Fermi energy. However, in higher-order, spin-resolved
topological insulators it is the spectral gap of the spin-spectrum, in addition
to the bulk mobility gap, which protects the non-trivial topology of the ground
state. In this work, we show that these two gaps, the bulk electronic and spin
gap, evolve distinctly upon introduction of disorder. This decoupling leads to
a unique situation in which an Anderson localization transition occurs below
the Fermi energy at the topological transition. Furthermore, in the clean limit
the bulk-boundary correspondence of such higher-order insulators is dictated by
crystalline protected topology, coexisting with the spin-resolved topology. By
removing the crystalline symmetry, disorder allows for isolated study of the
bulk-boundary correspondence of spin-resolved topology for which we demonstrate
the absence of protected edge and corner modes in the Hamiltonian and yet the
edge modes in the eigenstates of the projected spin operator survive. Our work
shows that a non-zero spin-Chern number, in the absence of a non-trivial
$\mathbb{Z}_{2}$ index, does not dictate the existence of protected edge modes,
resolving a fundamental question posed in 2009.
