Write a story that begins with someone unexpected coming into a character's life — or back into it: A past paramour takes residence in the next cubicle. A long lost sibling moves into the house next door. A green-skinned man who speaks no known human language appears in the backyard. Take it from there.
Ulterior motive
At the heart of every good story is change. A surprise appearance can be an effective catalyst for change. What will your character learn about life, or love, or himself because of this unexpected visitor? Who will change more, the main character or the visitor? Your options are myriad.