They have explored all avenues and see no way out of their difficulties. They feel there is nothing left for them but annihilation and emptiness.
Whereas people in a Gorse state decide to give up when there are possible solutions untried, the person in a Sweet Chestnut state is genuinely at the end of the line: theirs is appalling, final despair.
In this extreme state, the remedy helps us remain masters of our lives, and renews our hope and strength. Sometimes a way ahead may open even when we expect it least.