This is SUCH a hard topic. I totally get where you are coming from, no one should be faced with that kind of heavy responsibility when they haven’t invited it or been trained to handle it. Unfortunately, I’d venture to guess that some of those people who send the emails don’t have anyone else to reach out to and are desperate. Maybe this is shirking their responsibility, but I think in a lot of cases they aren’t even able to see that.
Still, it sucks that it falls on your unexpecting shoulders. And, I think it’s really good that you’re recognizing your boundaries and writing about them to hopefully help people understand what it’s like from your end.
I think if I were in that position I’d probably develop a canned response that included resources like Crisis Text line where the person could reach out for immediate, anonymous support from a trained crisis counselor. The worst part (to me) is that you get this information from someone about what they want to do or are going to do, and there isn’t really anything you can do other than steer them elsewhere, and I’m guessing you don’t get any sort of closure at all about it.