  We present a paradoxical finding that, in the vicinity of a topological phase
transition in a quantum anomalous Hall system (Chern insulator), topology
nearly always (except when the system obeys charge-conjugation symmetry)
results in a significant extension of the edge-state structure beyond the
minimal one required to satisfy the Chern numbers. The effect arises from the
universal gapless linear-in-momentum Hamiltonian of the nodal semimetal
describing the system right at the phase transition, whose form is enforced by
the change of the Chern number. Its emergent approximate chiral symmetry
results in an edge-state band in the vicinity of the node, in the region of
momenta where such form is dominant. Upon opening the gap, this edge-state band
is modified in the gap region, becoming "protected" (connected to the valence
bulk band with one end and conduction band with the other) in the topologically
nontrivial phase and "nonprotected" (connected to either the valence or
conduction band with both ends) in the trivial phase. The edge-state band
persists in the latter as long as the gap is small enough.
