(3.1) Let $X$ be a maximally degenerate Calabi-Yau variety and let $\mathscr{X}$ be a good minimal dlt-model of $X$ with reduced special fiber. Then we will see in Corollary 4.6 that $\mathscr{X}$ satisfies assumption (2), so that it gives rise to a non-archimedean SYZ fibration $\rho_{\mathscr{X}}\colon X^{\mathrm{an}}\to\mathrm{Sk}(X)$ in the sense of Definition 2.5. The principal aim of this article is to study the fibers of $\rho_{\mathscr{X}}$. In the classical SYZ conjecture, the fibers of the SYZ fibration are expected to be special Lagrangian tori away from a codimension two subset of the base. We will now present the corresponding structure in non-archimedean geometry, which was introduced in [KS06, §4.1].