Was he threatening her with suicide?

If so, I think a "Go for it." may be the best response. If the suicide is a way to provoke, it may be best to say you are not receptive. If it's a way of sending a message to be validated by her, then it might still be the better type of response. But it may not be.

Both might have been manipulating each other. You could argue she was manipulated into manipulating him.

If he doesn't have a PD you are unlikely to convince someone to commit suicide, I think. Not like that. But I'd think they both have/had one. Otherwise, there won't be a strong enough causality, I'd say. But I might be wrong. The most powerful manipulations are compulsions. She should be treated for that. To realise why she does it and how to change her behaviour.