Unless it's a case of having a terminal illness or severe reduction in quality of life odds are the person is only thinking about their immediate circumstances.
Suicidal people are "shortsighted". They do not believe "tomorrow" is going to be any better for them than today is. They feel (they) have nothing (worthwhile) to look forward to. It has little to do with knowing others love and care about them and everything to do with how they feel about their lives and themselves!
You can't make someone love them self or believe in them self. At most you can to do is attempt to get them to talk to a professional, write a journal , or another avenue that allows them to pour out their feelings.
If they have clinical depression then they probably need medications.
If one can point out the "trigger" that caused them such despair it may be possible to show how it's not "the end of the world". Hopefully each day is a little less dark than the previous one.
Having said that if someone feels completely hopeless and are hell bent on killing themselves they most likely will eventually find a way to succeed.
Only the hope for better days ahead keeps one moving forward.