In 'vanishing love fanfiction', it's likely about a love that gradually vanishes. It could be in the form of a tragic love story where the characters' love deteriorates over time. For example, in a fanfiction based on a fantasy series, the two lovers might be separated by a powerful magic spell that slowly erodes their feelings for each other. It gives fans a chance to explore different aspects of love and loss within the framework of their favorite fictional universes.
I'm sorry I can't directly recommend specific 'vanishing love fanfiction' works as there are so many different fandoms and platforms out there. But you can start by looking on popular fanfiction websites like Archive of Our Own. Just search for the term 'vanishing love' along with the name of the fandom you're interested in, and you'll likely find some relevant works.
It's not based on a true story. The plot and characters were invented by the writers for entertainment purposes. There are no real-life equivalents or incidents that inspired it.
Definitely not. The vanishing of the sun is a concept usually found in science fiction or fantasy, not in reality. There are natural processes that govern the sun's existence and behavior, and vanishing is not one of them.