Keep in daily touch (more when it seems warranted). Tell her outright that you are worried about her, knowing her history, don't let her dismiss it---the fact is, it is easier to commit suicide when someone you know/care for has done it.
Be an ear, let her say whatever she wants without judging (don't worry too much about giving positive feedback, don't give positives for each negative, don't try to cheer her up except as it comes naturally; listen, acknowledge the feelings...
and, as able, the fact that feelings and actions are not the same thing.
If the two of you share humor in your relationship---USE IT. Do not fear it. Great humor is often born of, and balm to, great pain.
The knowledge that her cousin could have survived this time as she had many other times of terrible pain is very difficult to deal with (guilt, shouldawouldacouldas abound---rage(bring her back I'll kill her myself)----and such sorrow, loss not just of a person but of a shared life that will not be---dreams lost---expectations (some not even known now) not met...
If there is any way you can, visit her in person.
Send, small tangible reminders of your presence. You know her and what she values.
Let her know, also, that, should she be suicidal and too down to call a stranger, that she can call you, and then you call the nearest ER (she either gets herself there, or you call the ambulance)----[I actually did this once long distance; half-way cross country...successful]---
Hang in there.
Hope your friend has a good t.; if not, she should get one that deals with mental health And grief issues. Even attendance at a peer group (survivors of suicide) may be an option (all depends on what type of "help" your friend finds actually helpful)
---in time, perhaps she will find a way to expand her cousin's inspiration---5k runs in the cause using her name--passing on the healthy lifestyle enthusiasm...
Sorry to ramble. Take what might help, leave the rest.
And, do not forget, this is a loss for you, by default. It does affect you.
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