Earlier quoted context omitted.
I've volunteered fairly regularly on one of the member hotlines, and have personally attempted suicide. Out of 1000 calls I had one person attempt, maybe 10 people decide not to attempt, and the rest were just people who were anxious or sad or scared and were having thoughts. There's a very broad spectrum, and for someone who is hopeless or just lonely and sad, talking to a caring human who listens and is comfortable…
It will be also great if you can briefly outline some of the things you tell them. I can't imagine the responsibility on the shoulders of a person who is trying to save a life at the other end of the line. Thank you for your service.
At some level, what people really want ultimately isn't an idea, it's a feeling, and learning how to soothe people is usually about being calm and attentive. The people who want me to provide them a solution to their problem usually get angry because I keep redirecting them back to their own feelings, and then we talk about the anger and see if they can find a way for that anger to not be the end of the conversation.
Sometimes though it's a bit different. The self harming teenager in foster care, for example, responds really well to people not getting upset. People that cut themselves are used to adults freaking out, so for self harmers it's usually some variant of "oh man, I'm sorry. Is the bleeding managed? Glad to hear. ... Hard day?"