In the exact setting there is no closed holomorphic curve. The failure of ‘somewhere boundary injectivity’ is often associated with multiple cover issues, namely $u:\Sigma\to X$ may decompose into several domain components, each of which factorizes through a somewhere boundary injective holomorphic disc (cf. [50] for the case of Lagrangian boundary with no corners).

In the simplest case, if $u$ factorizes through another disc, then the corner points would be repeated several times on $\partial\Sigma$. This phenomenon does not happen for the curves appearing in the bordism current $\mathcal{C}$, which involve only one corner at $CF^{0}(L,L^{\prime})$ and one corner at $CF^{0}(L^{\prime},L)$. Nor does this occur for teardrop curves, which have only one corner at a degree two self intersection point. This raises hope that the failure of ‘somewhere boundary injectivity’ may be highly nongeneric, or in certain situations can be ruled out altogether.