A Moishezon manifold is projective if and only if it is Kähler. This is no longer true for a singular Moishezon space. Moishezon proved projectivity criterion for Moishezon spaces with isolated singularities, and for rational singularities it is Known also.

So this is natural to ask Moishezon space with canonical singularites in the sense of MMP is projective iff it is Kähler?

Is the following statement true in general?:

Let $M$ be any compact complex variety with canonical singularities. Then $M$ is a Moishezon space if and only if there is a proper analytic subset $S⊂M$, such that $M\setminus S$ admits a complete Kähler-Einstein metric with negative Ricci curvature.

In fact the existence of KE for varieties of general type with mild singularites has been verified, so this question can be natural to ask

The motivation is the mild singular version of my recent question

Definition:A compact complex space $M$ is Moishezon if and only if there exists a weakly positive coherent $\mathcal O_M$-module of rank 1 on $M$.