Geometric conjecture for potentially dense subvarieties of singular varieties of general type

Let $X$ be a $\mathbf{b}{Q}$-Gorenstein variety with a canonical divisor $K_{X}$ big. A closed subvariety $Y\subset X$ is potentially dense if, after a finite extension of the base number field, its rational points are Zariski dense in $Y$. Let $\operatorname{NonC}(X)$ denote the non-canonical locus of $X$. Geometric conjecture. There exists a proper closed subset $Z\subset X$ such that for every potentially dense closed subvariety $Y\subset X$, either $Y$ is contained in $Z$ or $Y$ intersects $\operatorname{NonC}(X)$. This generalizes Lang's conjecture from smooth varieties of general type to varieties with canonical singularities, while allowing potentially dense subvarieties to meet the non-canonical locus. Its resolution status is not specified in the source.