I definitely wouldn’t let some random stranger (be it a man or woman) alone in my house, much less let them sleep there with only us two, and even much much less after seeing that they might be suicidal. Like, it doesn’t matter how “pretty/handsome/troubled/whatever” the other individual is, it just is a bad idea, I don’t even have to bring “culture” or “law” here, this is more about self-preservation, you should not trust strangers (especially one that openly admitted to have used some dubious methods to find where you live).