Suppose $U\subset\overline{U}^{\rm hyb}(\mathcal{X})$ is a Morgan-Shalen-Boucksom-Jonsson compactification associated to an arbitrary dlt stacky pair $(\mathcal{X},\mathcal{D})$ of boundary coefficients $1$ ([Od16]) with $\mathcal{U}:=\mathcal{X}\setminus\mathcal{D}$, its coarse moduli space $\mathcal{U}\to U$. Then for any holomorphic morphism $\Delta^{*}:=\{z\in\mathbb{C}\mid 0<|z|<1\}\to\mathcal{U}$ which extend to $\Delta:=\{z\in\mathbb{C}\mid|z|<1\}\to\mathcal{X}$, it induces a continuous map $\Delta\to\overline{U}^{\rm hyb}(\mathcal{X})$, i.e., the limit exists. Furthermore, such possible limits in $\Delta(\mathcal{D})$ are characterized as points with rational coordinates.