If this is self-harm (or voluntary disappearance for reasons unknown/personal troubles), I sure do hope the family was given an indicator like that. As hard as that would be, they would know.
I do think that there are people (who self-harm or go voluntary missing) who are of the mindset that it's better that family/friends never really know for certain -- that somehow, not knowing is more kind, in wanting to ease any unwarranted feelings of guilt their loved ones may have at not realizing they were having serious problems...and perhaps some also don't want their loved ones final thinking about them to be negative (their "leaving" decision)...
But I think it's human nature to want/need closure... whatever the truth is - people would rather know. Then those left behind can grieve, and learn how to cope and move on, as they must.
Hope is a wonderful thing and the best motivator -- *if* there is a real reason to hope, as in a possibility of a loved one's return... but if it's false hope, that is a swirling haze of confusion/ongoing limbo that often takes a great toll on people... I'm not sure everyone who "leaves" fully understands this (and I do understand that logical thinking is not always possible at that point, so I'm not blaming -- just recognizing what a painful issue this becomes for too many).
I'm always left feeling that anxiety/depression, whether situational or chronic (or other mental health issues) need to be talked about SO much more in society... we need to be more open and real about it, so nobody need feel shame at saying what is really going on. The HOPE aspect needs to be focused on the front-end, in ensuring people who struggle can feel they can get comfort and help -- that all is not lost. We all have problems, no matter what they are. I hate that some get to a point where they feel leaving, in whatever form that takes, is their best option.
I'm confident all family/friends would give anything to have an opportunity to intervene with a loved one who is greatly struggling...and get to the helping phases.
If there is the remotest chance Paul is out there, I pray he contacts his family. If not, I hope they have their closure. I'm so sorry for them going through this.