Whilst undertaking a training Captain course, we students were told that should any psychological problems emerge with our trainees we were "not to go there" and to tell them to seek professional help. Issues such as past abuse or alcoholism could come to light and we could easily make things worse by having a go at a problem we weren't trained to deal with.
Talking once seriously, or a few times jokingly about suicide means that person needs help and it's up to mental health professionals to provide that help. Immediate grounding is the only option for a pilot and it's up to the medical department to take it from there.