  Two-dimensional higher-order topology is usually studied in (nearly)
particle-hole symmetric models, so that an edge gap can be opened within the
bulk one. But more often deviates the edge anticrossing even into the bulk,
where corner states are difficult to pinpoint. We address this problem in a
graphene-based $\mathbb{Z}_2$ topological insulator with spin-orbit coupling
and in-plane magnetization both originating from substrates through a
Slater-Koster multi-orbital model. The gapless helical edge modes cross inside
the bulk, where is also located the magnetization-induced edge gap. After
demonstrating its second-order nontriviality in bulk topology by a series of
evidence, we show that a difference in bulk-edge onsite energy can
adiabatically tune the position of the crossing/anticrossing of the edge modes
to be inside the bulk gap. This can help unambiguously identify two pairs of
topological corner states with nonvanishing energy degeneracy for a rhombic
flake. We further find that the obtuse-angle pair is more stable than the
acute-angle one. These results not only suggest an accessible way to "find"
topological corner states, but also provide a higher-order topological version
of "bulk-boundary correspondence".
