we shouldn't force suicidal people into hospitals. I honestly think its inhumane to do so, because many people have talked about just how traumatizing involuntary hospitalization is, and think about it, your being driven somewhere whether you like it or not, you have no say in whether you get to go and you'll be forced to stay there against your will for several days or weeks, don't know anyone, your sources to contact the outside world or entertain yourself are limited, and you have to tell someone you don't know about deeply emotional and personal struggles in your life, when you're already in so much distress that you wanted to end your own life. I don't think that sounds like a good time, and people who've experienced have described as traumatizing. I think the only reason people are okay with forced hospitalization of suicidal people is because suicidal people, like a lot of other mentally ill people, aren't seen as full humans. If someone is going to hospitalize someone against their will because they're suicidal, they're not a safe person.
If you want to know how to help a suicidal person, first of all, LET THEM DECIDE IF THEY THINK A PSYCHIATRIC HOSPITAL WILL HELP. If they think it will, and want to go, then help them get to the best one they can find. If they don't think it will and don't want to, then don't make them.
Speaking based on testimony from other people who've been suicidal and as someone who's been suicidal, if the hospital is ruled out, here's how you can help; stay by their side, but give them space when they say they need it. They're probably very lonely and don't think anyone will care or listen to them. If they need to talk, listen, if they just need company or to get their mind off things, then offer to keep them company, however the feelings they're probably experiencing are likely to overwhelm them and there will likely be times where they need space. Give them their space when they need it, but do check on them from time to time.
offer to do chores around the house for them. They're already overwhelmed by whatever's going on in their life and might lack the energy or motivation to do chores, even basic ones. I can't tell you how much easier it would've been during those times where i was the closest to ending it, if someone had just asked to clean my room for me, or offered to do the vacuuming for me, or even made my fucking lunch for me. It's going to take the load off for them while they're trying to make it through whatever they're going through that put them in this state.
This is pretty important, do try and remove any sharp objects from their vicinity or just generally objects they could use to harm or kill themselves. It might even be helpful to keep an eye on them if they do need to use those objects for whatever reason.
In general just offer to listen to them and help them, and keep them company. Play their favorite game with them, watch their favorite show with them, etc. and make sure to check on them at least semi-frequently until they can get back on their feet. Make them feel safe and listened to, don't force them into a place or situation they don't want to be in, because doing that will make it worse.