As 4get says- if she wanted to kill herself she would be dead by now- this is someone whose feeling wretched who wants somthing to replace that which she has lost and she is doing this by harming herself ( self reproach and guilt) and drawing attention to herself ( gaining love and sympathy by her actions).
the real danger here is that this sort of behaviour can become addictive, the massive pitches of mood and emotion it brings are very compelling for someone whose numb with grief about the demise of their relationship.
As I doubt it's true depression then I think it's a good thing that she hasn't been prescribed anything- they generally don't help, and certainly not if you are just suffering from terminal low self esteem issues.
What your friend actually needs is a measured plan drawn up whereby she starts to regain calm control over her life again eradicating whoever it was that dumped her systematically and replacing it with other things that are life enriching. If she's not prepared to do that, and she probably isn't, friends are left to make a choice of whether to do it for them, or back off.
My advice is not to pander to endless moaning conversations about ex bf etc and only engage in positive situations with her like going out, arranging holiday etc, talking about new job, brighter future. Her self esteem is the only issue here, and that's what has to be addressed iderally through counselling, meditation etc certainly not through drugs.Somtimes you do have to be slightly cruel to be kind and I think here is your final chance to do that before your friend simply spends her future repeating a pattern.