Non-vanishing conjecture for lc pairs

Let $d$ be a positive integer. Let $(X/Z,B)$ be an lc pair of dimension $d$, and suppose that $K_X+B$ is pseudo-effective over $Z$. Write $|(K_X+B)/Z|_{\mathbb R}$ for the relative real linear system.

Non-vanishing conjecture. The relative real linear system is nonempty:

$$|(K_X+B)/Z|_{\mathbb R}\ne\emptyset.$$

This conjecture is weaker than the good minimal model conjecture and is a fundamental non-vanishing problem in the minimal model program. Its status is not resolved in the supplied source context.