Somewhere in the City
There is a woman who just woke up, as she does every morning. She has the day off of work, and it's a sunny day, so she will spend the morning reading in her living room.
After a light lunch she will go downstairs, check the mail, and think for a moment about going out to the store. Money is tight, though. So she decides instead to talk to her neighbor for a few moments before going back up to her apartment to finish her book. She will drift off to sleep once or twice during the afternoon, but around six she'll finish the book and close it quietly. Then she'll go to the kitchen to make herself a simple dinner. While she cooks she will hum softly, just to have some sound. After dinner she'll turn on the television for a bit, then go to bed, a quiet, perhaps dull, but peaceful day behind her.
And, because of the eccentricities of time, she will do this every day forever, as she has been doing it for sixty years.
Somehow her quiet path through the day formed a closed loop, instead of a spiral like everyone else. Somehow a remnant of those actions has become stuck, her personality flowing around that circle day after day, following an identical path around the Earth's axis every 24 hours.
Outside of that closed loop the building has changed. Someone else lives in that apartment now, there's a different neighbor downstairs. But she still follows her course, her quiet, peaceful day projecting only slightly into a world that has forgotten her. Her closed loop doesn't interact with the world anymore. But sometimes, around six o'clock, there's a faint sound of humming in the kitchen. And when the sun is just right there is a quiet sense of contentment in the living room.