A countable group has the strong topological Rokhlin property (STRP) when the topological space of its actions/dynamical systems over the Cantor space admits a residual conjugacy class. Kechris and Rosendal established that the group of integers has the STRP, and a classification of countable groups having the STRP remains an open problem. The goal of this talk is presenting a sufficient condition for the failure of the STRP in terms of subshifts of finite type with specific properties. This is based on the recent preprint https://arxiv.org/pdf/2601.03501.