So, I have to say that this is one of the things I've been most looking forward to - the addition of concrete backstory elements in character creation was great, but the suggestion if not mandate to mess with these in some way when characters go insane is a fantastic.
So, I had three characters go insane last session (two temporarily and one indefinitely) - so here is how I resolved to amend thier Backstories.
Luigi, the Mafia hitman, was the simplest. He's a Honorable as a trait, so I simply added the PC who slew the Opener of Ways (Dimensional Shambler) as an Important Person because he now owed his life to this man. It's basic, kind of boring, but will continue to provide the character a hook to continue with this group once the initial adventure is finished.
That man, Henry, the Handyman started off the game with a phobia of zombies and the walking dead (Backstory, as combination of his War Experience and Mythos Experience he witnessed the dead rising in the trenches) so I actually added a scar to his story - a mysterious, large Y-shaped scar that spans his torso. He can't really remember when or where he got it, probably the Great War, he just knows that he doesn't like thinking about it and tries to ignore it all the time...
This ties into this characters secret pulp nature that I have not revealed to the player, but that from the look on his face he probably guessed at least part of it when I told him this.
Lastly, Helen, the Antiquarian, has gone indefinitely insane. She almost died, but blew all her Luck (ala the Pulp rules) to prevent this from happening, but was also essentially drenched in the blood and ichor from the Opener of the Ways. Her Backstory was amended with the note in Encounters with Strange Entities: "The Opener of the Way, it killed me, but I passed through it and I did not die."
For this character this actually lets me start to build up a pulpier character (and/or watch her descend into madness and worse) and I plan to start building up some abilities that riff off her comingling of blood and essence with said Opener of Ways. The player struggles a bit with role-playing, so I'm hoping that this provides some meat for her Investigator/Hero to grow and be more than simply a researcher.