  In a recent paper, Gorbenko and Zan [arXiv:2005.07708] observed that $O(n)$
symmetry alone does not protect the well-known renormalization group flow from
the dilute to the dense phase of the two-dimensional $O(n)$ model under thermal
perturbations. We show in this paper that the required "extra protection" is
topological in nature, and is related to the existence of certain
non-invertible topological defect lines. We define these defect lines and
discuss the ensuing topological protection, both in the context of the $O(n)$
lattice model and in its recently understood continuum limit, which takes the
form of a conformal field theory governed by an interchiral algebra.
