  We show that a four-manifold admits a boundary Lefschetz fibration over the
disc if and only if it is diffeomorphic to $S^1 \times S^3\# n
\overline{\mathbb{C} P^2}$, $\# m\mathbb{C} P^2 \#n\overline{\mathbb{C} P^2}$
or $\# m (S^2 \times S^2)$. Given the relation between boundary Lefschetz
fibrations and stable generalized complex structures, we conclude that the
manifolds $S^1 \times S^3\# n \overline{\mathbb{C} P^2}$, $\#(2m+1)\mathbb{C}
P^2 \#n\overline{\mathbb{C} P^2}$ and $\# (2m+1) S^2 \times S^2$ admit stable
structures whose type change locus has a single component and are the only
four-manifolds whose stable structure arise from boundary Lefschetz fibrations
over the disc.
