  A sofic group $G$ is said to be flexibly stable if every sofic approximation
to $G$ can converted to a sequence of disjoint unions of Schreier graphs by
modifying an asymptotically vanishing proportion of edges. We establish that if
$\mathrm{PSL}_d(\mathbb{Z})$ is flexibly stable for some $d \geq 5$ then there
exists a group which is not sofic.
