Right after I put my question in words, which was useful for myself to tackle my own concern, I started thinking of it, and found some answers/comments to my own question that I list here for the sake of the topic.
You can paint a canvas or write a book and submit them to the appropiate gallery. That is meant to persist and, if good enough, have a value, both in money and in meaning for both the author and the potential owner who buys it.
There will be politics, so an elected governor should remain for a certain time, and that should mean something along the history of events.
I don't really think we'll be allowed to leave our stuff on the floor while in the street, just like that. Not at least without some control. Imagine the mess that could be? But I think it's one of the most interesting elements of players interaction. As facade and Capped say, it could be very useful for criminals. But for police too in case whatever object dropped in the crime scene can serve as an evidence. I imagine the clutter being cleared by the corresponding cleaning service every once in a while.
These are the things that will make each day consistent with the previous, and set the basis of the next one. These are the things I mean when talking about persistence.