I'm not entirely sure specifically as it could be a wide range of things. It might be a story by John Gibson. Maybe it's a personal account, a news piece, or a fictional work.
There's a chance that Big John is a unique character created by the Fallout 4 community. Maybe he was part of a mod or some fan - made content that added this sad story to the game's lore. Without more context, it's hard to say exactly who he is, but he's likely a character within the Fallout 4 universe that has a particularly sad narrative.
I'm sorry, I don't know the specific 'Big John story'. There could be many stories named after someone named Big John. It could be about a local hero, a character in a community, or perhaps a fictional creation in a particular book or folklore.