Min-cut in a network with zero flow from source to sink

Question

The max-flow min-cut theorem guarantees that the min-cut of a directed network equals the maximum flow. And we can compute $S$ and $T$, are disjoint subsets containing source node and sink node respectively from the residual graph.

What will be $S$ and $T$ if the max-flow from source to sink is 0, that is, there is no directed path from $s$ to $t$? Is $S$ going to be the singleton set {s} or its the empty set $\phi$ and $T$ be the vertex set $V$?