Weak square and stationary reflection

It is well-known that the square principle □ _λ entails the existence of a non-reflecting stationary subset of λ⁺, whereas the weak square principle □λ∗ does not. Here we show that if μ^cf(λ) < λ for all μ < λ, then □λ∗ entails the existence of a non-reflecting stationary subset of Ecf(λ)λ+in the forcing extension for adding a single Cohen subset of λ⁺. 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 □λ∗ for every singular cardinal λ of countable cofinality.