  In non-smooth stochastic optimization, we establish the non-convergence of
the stochastic subgradient descent (SGD) to the critical points recently called
active strict saddles by Davis and Drusvyatskiy. Such points lie on a manifold
$M$ where the function $f$ has a direction of second-order negative curvature.
Off this manifold, the norm of the Clarke subdifferential of $f$ is
lower-bounded. We require two conditions on $f$. The first assumption is a
Verdier stratification condition, which is a refinement of the popular Whitney
stratification. It allows us to establish a reinforced version of the
projection formula of Bolte \emph{et.al.} for Whitney stratifiable functions,
and which is of independent interest. The second assumption, termed the angle
condition, allows to control the distance of the iterates to $M$. When $f$ is
weakly convex, our assumptions are generic. Consequently, generically in the
class of definable weakly convex functions, the SGD converges to a local
minimizer.
