Let $X$ be a finite, regular CW complex, and let $X'$ be its barycentric subdivision (i.e. the order complex of the face poset of $X$). Assume $X$ is collapsible.
Is $X'$ collapsible? Is $X'$ non-evasive?
By Theorem 2.10 of Welker the answer to both questions is positive if $X$ is a simplicial complex. But what about more general, regular CW complexes? I believe at least the first question has a positive and well-known answer, but is it stated explicitly anywhere in the literature?