The preperiodic-closure conjecture for polarized dynamical systems

Let $(X,f,\mathscr L)$ be a polarized dynamical system over an algebraically closed field of characteristic zero. Let $Y$ be an irreducible subvariety of $X$, and let $Y_0$ be the Zariski closure of the set of preperiodic points of $X$ that belong to $Y$. Preperiodic-closure conjecture. Are the irreducible components of $Y_0$ preperiodic subvarieties? The question is posed as a converse to the density of preperiodic points in a preperiodic subvariety; the source notes that recent counterexamples prevent an unconditional affirmative formulation and leaves this question open.