find the union of all min cuts of a flow network
Note $S_{\max}=V-\bigcap_{S\in\mathcal{F}}(V-S)$. And $\bigcap_{S\in\mathcal{F}}(V-S)$ is the set of all vertices from which $t$ is reachable in the residual graph.

The reason why $\bigcap_{S\in\mathcal{F}}(V-S)$ is the set of all vertices from which $t$ is reachable in the residual graph is the same as the reason why $S_{\min}$ is the set of all vertices that are reachable from $s$. You can prove this using the complementary slackness conditions.