I have the following basic question. Everything is over $\mathbb{C}$.

Let $X$ be a hyperkähler (irreducible holomorphic symplectic) variety and we consider a small contraction $f\colon X \rightarrow Y$. By this I mean that f is birational and surjective (e.g. induced by a big and semiample line bundle) and the exceptional locus $B$, i.e. the locus where $f$ is not an isomorphism, has codimension $\ge$ 2. Is $B$ uniruled?

If B is an irreducible divisor, this is true and follows from Section 1 of Huybrechts - Compact hyper-Kähler manifolds.

However, I could not find a statement in the case that $B$ is not a divisor. The only statement I was able to find is that each irreducible component of $B$ is algebraically coisotropic (Theorem A in https://arxiv.org/abs/math/0111089).

Is more known about the structure of $B$?