  It is well-known that the square principle $\square_\lambda$ entails the
existence of a non-reflecting stationary subset of $\lambda^+$, whereas the
weak square principle $\square^*_\lambda$ does not. Here we show that if
$\mu^{\mathrm{cf}(\lambda)} < \lambda$ for all $\mu < \lambda$, then
$\square^*_\lambda$ entails the existence of a non-reflecting stationary subset
of $E^{\lambda^+}_{\mathrm{cf}(\lambda)}$ in the forcing extension for adding a
single Cohen subset of $\lambda^+$. It follows that indestructible forms of
simultaneous stationary reflection entail the failure of weak square. We
demonstrate this by settling a question concerning the subcomplete forcing
axiom (SCFA), proving that SCFA entails the failure of $\square^*_\lambda$ for
every singular cardinal $\lambda$ of countable cofinality.
