One possible theme is unrequited love. Snape loved Lily deeply, and their Patronuses, both being doves perhaps in some fanfictions, could symbolize that love. His Patronus could be a constant reminder of his love for her, even though she was with someone else.
In a fanfiction, Snape's Patronus could be the key to saving Lily from a dark magic curse in an alternate universe. Since the Patronus represents love and protection, Snape's doe Patronus might be able to break the curse that has trapped Lily's soul. As he sends his Patronus towards her, it glows with a powerful light that gradually dispels the dark magic surrounding her.
There were stories about guardians in different types of novels, but the most popular novels recently were "Invasion of the Myriad Races: All the People Fight, Guardian God of the Nine Regions","I Am the Guardian God of the Human World in the Wilderness","The End of the World, I Am the Guardian God of the World", and "The Strongest Guardian God of the End of the World". I hope you like my recommendation. Muah ~
Well, usually when we hear 'John Doe', it's more of a fictional or anonymous reference. But there might be rare cases where it refers to an actual person if it's in a very specific and local context that we don't know about.