When are left perpendicular categories of module categories nonempty?

Question

Let $\Lambda$ be a finite dimensional hereditary algebra over algebraically closed field $k$. Let $\mathcal{C}$ be a full extension-closed Abelian subcategory of $mod \Lambda$ closed under direct summands and extensions that isn't $mod \Lambda$. Let $^{\bot}\mathcal{C}$ be the left perpendicular category of $\mathcal{C}$. Why is $^{\bot}\mathcal{C}$ nonzero?

Answer 1

Edited: This answer is currently incorrect. I will fix it once it gets corrected.

This is in fact a known result by Ingalls and Thomas (https://arxiv.org/abs/math/0612219) who proved the statement in Prop 2.24.