Let $G$ be a linearly reductive algebraic group acting regularly on an affine space over $\mathbb{A}^n$ an algebraically closed field $\mathbb{K}$. Let $Y$ be a $G$-invariant (closed) affine subvariety of $\mathbb{A}^n$.
Are there papers where people have studied when can we expect $Y$ to be NOT an orbit closure?
I'm interested in the setting of quiver with relations such the associated finite dimensional algebra $A$ is brick infinite, i.e., there are infinitely many non-isomorphic bricks. In this setting $G$ is the product of general linear groups acting on the representation space of the underlying quiver (an affine space) and $Y$ is an irreducible component of the representation space of the quiver with relations.
