I have seen cases similar to what you describe here. In one case, the 'missing person' called Law Enforcement and said ' I am fine, stop searching for me.'
And they did, after they sent an investigator out to verify it was him, and he was not under duress. The p0lice then called the family, said he was Okay, but didn't want to be contacted. The End.
I am sure it was painful for the family, but not as bad as looking forever and imagining they were murdered.
One of the cases we were following here ended up in a similar way---the young man from San Diego area, who was going to a Brony convention, then disappeared, vanished in thin air. Eventually he called someone and said he was fine, just needed to get away. All of the publicity and searching stopped cold.