I'm confused between the title and the post. Not sure if you're talking about being approached by someone who is experiencing suicidality and depression, or doing the approaching.
I wouldn't approach someone because they can't fix me or carry my burdens, I would want those things resolved first. Otherwise, it will turn into a co-dependence scenario with conflict over who is responsible for whom and for what issues. I own my own shit and don't want another trying to own it for me or to fix me, and I find it hard to imagine that someone could build emotional intimacy with me and be able to not take any of that on. Therefore, I'd have to question why they'd be willing to get involved if not to try to make me into something I'm currently not. If they're okay with me feeling that way and still being intimate with me, I'd wonder what they're getting out of it. It just feels like a recipe for a whole mess of enmeshment or enabling of sick motivations and behaviors, just one big ball of yuck that will keep growing like yeasty bread in an oven, or perhaps more like a souffle with hopes of it being tasty, but is only going to grow, blow up, get scorched, and collapse.
If someone approached me who was experiencing those things, I would decline. Those are heavy and consuming issues they bring, and while I have compassion for them, getting emotionally intimate means getting emotionally intimate with their issues. I already have enough of my own heavy stuff to deal with. Even if we had like issues, being "equally yoked," I think we'd be more likely to pull each other down than lift each other up. I don't want to get yoked to more suffering in the false hope it will bring comfort to do so.