After you finish the game/route and restart it for new play-through, (a) new event(s) which previously didn't exist is(are) inserted at random points(mostly in common route),

They are mainly used
-to present the readers with more details about the story with each playthough
-as a progressive foreshadowing of the true route which typically require multiple playthroughs to unlock.
-simply as a "bonus event".

Do not mix this with Unlockable Side Stories. Unlike side stories which exist as "bonus content" and need separate access, new events are naturally added to the overall story.