Alice turns out to be quicker than Bob, and stops him long enough to actually talk him down.
Bob is in no actual danger of dying (is only a short distance from the ground if about to jump, using children's medicine to overdose on, etc.), but Alice attempts to talk her out of it with as much panic as if she would die if she went through with what she is about to do.
Bob is not actually suicidal and his actions make sense in context, but Alice sees him, thinks he's going to kill himself, and attempts to talk him out of it.
Alice was actually trying to persuade Bob to go through with killing himself, but her words actually persuade Bob to not do it. Bonus points if Bob thanks her profusely for it.
Zig Zagged: Alice shows up to talk Bob out of killing himself. Bob starts to listen to her and decides not to do it—until Charlie shows up and taunts him into going through with it.
Averted: Bob decides not to kill himself before Alice shows up.
Lampshaded: "Have you come to talk me out of killing myself?"
Defied: Charlie stops Alice from talking Bob down because he wants Bob to kill himself.