Let $X$ be a quasiprojective variety over $\mathbf C$. Take the union of all projective subvarieties $W \subseteq X$ that have dimension at least $1$. Is the result Zariski closed?
(I was wondering this in the particular setting $X = \mathcal M_g$, where the projective subvarieties have been the subject of some study. But the general question seems natural as well.)