I am all for this being a public service but why is this up to the library? I understand it is usually a convenient, local place that people can easily get to, but I don't think most librarians are equipped to deal with someone who needs help in this kind of way. Much like guns shouldn't be a "hazard of the job" for school teachers, I don't think librarians should be responsible for this kind of public safety.
We should invest in community centers with resources for such things. Mental health professionals, trained social workers, public servants specifically trained to help those who might have stumbled along the way.