My parents have always been supportive of me and want nothing else but for me to live and enjoy living. I've been trying to get better again after my most recent suicide attempt but well, I've ran into the same wall of not being able to help myself and not being helped by the "help" provided to me.
I know how hard it is to lose a close family member, and after everything my parents have tried to do for me, I know they'd be devastated. I think my mom particularly would not be able to get back to a normal life because of it. I don't really have a good answer for you; I think in my case personally, killing myself would be a very egotistical act. The thing is though, there's nothing in life I find enjoyment out of anymore, and I haven't for several years. I'm stuck with just drifting through every day while my mental state declines, getting more entrenched in my issues. I've tried to explain it to them, but it only served to make them worry more and message me several times a day for weeks, which only served to stress me out.
In the end, I think if they could see it from my perspective, they'd understand why I don't want to live. If they could experience my daily life as I do, they'd see how much I have to give just to get nothing out of it. Staying a live is something I do for their sakes, to not ruin their lives. Killing myself is something I'd do for myself. It's the last thing left when there's nothing else I can do purely for my own gain. Living for the sake of others just doesn't cut it in the long run, the torment you yourself have to go through every day whittles you down until you don't have the strength to run on empathy alone.
When I die it'll be the last favour I'll do for myself. The last time I treat myself.
TL, DR: Can't really cope with it, it's a win-lose situation. You get to a point where the shit you deal with is just too much, and the cost outweighs the gain. Unfortunately, they'll have to live with it, however they can manage.