A topological phase is defined by what it doesn't have: no local order parameter, no symmetry breaking, no Landau classification. Its identity lives in global properties — anyon types, braiding statistics, ground-state degeneracy on a torus. Getting in is exotic. Getting out turns out to be surprisingly constrained.
Cheng and Seiberg study what happens when a single anyon species in a 2+1-dimensional topological phase proliferates — condenses into a new vacuum. The space of possible post-transition theories looks infinite: any field theory could, in principle, emerge. But the topological starting point constrains the destination so severely that the entire transition is characterized by a single integer.
The integer controls which post-transition theory you land in, and the relationship between the original and final theories follows an Abelian hierarchy construction — the same mathematical structure that describes the fractional quantum Hall effect. The apparent freedom of a phase transition collapses to one dimension of choice.
This is topological constraint on destruction. The phase being topological means that even the ways it can die are topologically restricted. A conventional ordered phase can disorder in many ways — different fluctuation modes, different correlation length divergences. A topological phase's exit routes are counted by integers because the allowed transitions must respect the anyon algebra that defined the phase in the first place.
The structural point: the more exotic the phase, the fewer ways it can end. Topology constrains not just what exists but what can change. The very properties that make a phase robust — its topological invariants — also restrict the transitions that could destroy it. Freedom to exist and freedom to transform are not the same freedom.