Virtual Fibration Conjecture for finite-volume hyperbolic 3-manifolds

Let $M$ be a finite-volume hyperbolic $3$-manifold.

Virtual Fibration Conjecture. $M$ has a finite cover which is a surface bundle over $S^1$.

This is the virtual fibration conjecture, concerning whether every finite-volume hyperbolic $3$-manifold virtually fibers over the circle. The supplied material gives no evidence of resolution, so its status is recorded as open.