One that I've run into several times is suicide. Most of the time, the person isn't in immediate danger. I've been around when people were.

I'm not going to go into any detail for people's privacy, but it took over an hour to figure out who a regular member of a community was in real life and then get emergency services in another country to them. Got independent confirmation they got dragged to a hospital in time. They weren't exactly grateful afterwards, but they stayed in the community and didn't repeat the attempt.