What does your therapist say / do if and when you talk about offing yourself?

Not in the need-to-go-to-a-hospital-now kind of way -- because then the course of action is clear -- but just describing the feelings / thoughts?

ETA: My experience -- was told that listening to me was making her "physically sick" when I told her to stop saying whatever utterly useless (to my mind) stuff she was saying about my life.

Although of course she said I should go ahead and continue talking.

And, on and on in that vein.

Till I finally stopped trying to talk about it -- I joked some and then quit.

The whole experience made me wonder if therapists are trained to somehow rush to 'intervene' even when the obviously better (asked for by the client, even) path would be to not attempt to actively intervene?