I've seen it happen in FO3 (or NV, can't remember), I started a fight with a caravan guard i think (by accident). I put away my gun and he walked away.
Long ago in a galaxy far far away...
I have accidentally shot Diamond city guards, and the only way to get him non-agro, was to run away for a few days. Putting away my weapons did nothing.
I have actually done this before. Very rare that it works. It was with a low level scavenger near Sanctuary. I got too close and they shot me. One shot from my shotgun brought them down to about 25% health. I put away my weapon and so did they, saying "Ok, ok, you win just don't kill me" and then started walking away.
The problem is if you have a companion with you, even dogmeat. Even after the person surrenders, you will notice their health bar and name are still red meaning hostile. Your companion will continue to attack and start the whole process over again.
Solution............Kill em........Kill em all.....
Yeah, I got into trouble at Cambridge police station.
I like to whip Knight Rhys when i see him because he's so arrogant.
He takes a blow before turning red.
Anyway I was turning in a quest and did something that made the occupants see red.
I ran away slowly enough so they could follow me down the road to Graygarden where the provisioner and companion gave him and Scribe Haylen a whipping.
By not having a weapon drawn the BOS left me alone
I sure enjoyed seeing knight Rhys being flogged.
Anyway i went back later and all was forgiven.
Knight Rhys flogging.
https://youtu.be/miO-Om7A4K8