Generalized Lang conjecture for pre-periodic points

Let $X$ be an algebraic variety defined over a number field $K$, and let $f:X\to X$ be a surjective endomorphism defined over $K$. A point of $X$ is pre-periodic if its forward orbit under $f$ is finite. Let $Y$ be a subvariety of $X$ whose orbit

$$\{Y,f(Y),f^2(Y),\ldots\}$$

is not finite, so that $Y$ is not pre-periodic.

Generalized Lang conjecture. The set of pre-periodic points contained in $Y$ is not Zariski-dense in $Y$.

This is presented as a consequence of the general fractal conjecture and as a version of generalized Lang's conjecture. The source gives no resolution of this statement, so it remains open.