Non-rigid indecomposable summands of simple-minded collections in bounded derived category of hereditary algebras

Question

Let $\Lambda$ be a hereditary algebra over an algebraically closed field $k$. Let $S$ be one of the indecomposable summands of one simple-minded collection in $D^b(\Lambda)$. Is it true that $S$ is necessarily rigid? This is true when $\Lambda$ is of finite type. What about tame and wild types?