Should they go kill themselves? Funny that the mental failings of the jumper evoke such sympathy and the mental failings of the "asshole" evoke such hatred.
There's a significant qualitative difference between someone being self-destructive (albeit with traumatic consequences for those who are connected to them) and engineering the destruction of someone else.
There may be mental failings involved which are outside the control of the individual, but I don't think that's the whole story or we'd have to throw the idea of moral agency out the window (I picked the example I did because the person neither appeared nor claimed to suffer cognitive impairment AFAIK). We are actors as well as being acted upon by our environment and biology; insofar as our activities impact others, we have some responsibility to regulate them.
When visiting the US this summer, we walked across the Golden Gate (which at the time didn't have the "anti-suicide rails" that I believe are planned).
In several places there were both help phones and signs asking people to seek help, and also in one place there was graffiti on the pavement saying something like "somebody loves you". It was quite moving.
You have to find the will and reason to live yourself if you really think life is that grim that you have to end it I have only one thing to say to you make sure you are 100% certain about that and there's no other way out of your situation before you do it this is one of the few things that cannot be undone.
There's almost certainly better options you can try before doing this.
I can't politely express my opinion about people like this.