Minimal model conjecture for generalized pairs of relative log numerical dimension zero

Let $(X/Z,B,\mathbf{M})$ be a generalized log canonical pair (g-lc pair), where $X\to Z$ is a projective morphism of normal quasi-projective varieties, $B$ is a boundary $\mathbb{R}$-divisor on $X$, and $\mathbf{M}$ is a nef part with trace $\mathbf{M}_X$ on $X$. Suppose that

$$\kappa_\sigma(X/Z,K_X+B+\mathbf{M}_X)=0.$$

Minimal model conjecture. Then $(X/Z,B,\mathbf{M})$ has a minimal model.

The conjecture addresses the existence of minimal models for generalized pairs without an NQC assumption when the generalized log canonical divisor has relative numerical dimension zero. The surrounding discussion highlights that minimal model results are substantially better understood for NQC generalized pairs, while non-NQC pairs exhibit failures of generalized nonvanishing; the claim is presented here without a stated resolution.