Flat Closing Conjecture for proper CAT(0) spaces

Let $X$ be a proper CAT(0) space with a proper cocompact action of a discrete group $\Gamma$. A flat $F\subset X$ is $\Gamma$-periodic if some subgroup $\Gamma_0\leq\Gamma$ preserves $F$ and $\Gamma_0\backslash X$ is compact. Assume that $X$ contains a flat of dimension $n$. Flat Closing Conjecture. Does $X$ contain a $\Gamma$-periodic flat of dimension $n$? The conjecture asks for a converse to the flat torus theorem, which constructs flats from free Abelian subgroups of $\operatorname{Isom}(X)$. The source presents it as an open question and notes that, for discrete $\Gamma$, a periodic flat has a virtually free Abelian stabilizer of the corresponding rank.