Suicidal people nobody will know until they are dead. People who want attention and help will rarely die of an attempt. One has to differentiate with whom one is speaking.
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If they are truly suicidal, there is nothing that will prevent the inevitable.
This is factually incorrect. There are a lot of things that "make sense" regarding suicide and mental illness: that "cries for help" and successful suicide are inherently unrelated, that suicide is a determined goal of people who have made a rational choice based on their current value system that death is better than life, etc. The fundamental problems with those ideas are 1) they're inherently one-size-fits-all, which is rarely if ever the case in mental illness, and 2) their appeal derives from the fact that they "make sense" to us as rationally thinking people.
Yes, I'm sure there are some situations (insurance fraud by suicide, etc) where there is enough logic and determination behind the decision that lack of access to one method would only lead to another. But in many more cases, a combination of volition and access lead to suicide. That's why when the UK mandated that Tylenol only be sold in blister packs (rather than big tubs), successful suicides by Tylenol overdose decreased by 22%, liver transplants due to Tylenol overdose decreased by 66%, and non-fatal self overdose went down by 15% (BMJ 2001;322:1203). Similarly, gun availability correlates with suicide, even when controlled for rates of mental illness, etc. (Inj Prev. Jun 2006; 12(3): 178–182).
The point of this is not to advocate for Tylenol in blister packs or gun control legislation -- whether those liberty tradeoffs are worth preventing suicides is an entirely different question. The point is that this prevalent idea that "people who want to kill themselves will do it no matter what we do" is flawed, because it's based on the thought that "if I wanted to kill myself, I would do it no matter what anybody else did." But you and I don't share the thought processes that suicidal people have.
Re the "someone who attempts suicide was just crying for help and won't actually do it," the numbers are as follows (from UpToDate, possibly the best general medical resource out there aimed at physicians):
"The strongest single factor predictive of suicide is prior history of attempted suicide (Am J Epidemiol. 2008;167(10):1155). Patients with a prior history of suicide attempts are 5 to 6 times more likely to make another attempt; furthermore, up to 50 percent of successful victims have made a prior attempt (Arch Gen Psychiatry. 1983;40(3):249). One of every 100 suicide attempt survivors will die by suicide within one year of their index attempt, a risk approximately 100 times that of the general population (Hawton, K. Handbook of Affective Disorders, 2nd ed, 1992. p.635).
"Risk for completed suicide, following a history of suicide attempt, is greatest in patients with schizophrenia or unipolar [depression] and bipolar disorder (BMJ. 2008;337:a2205)."