Is there a word for something that does NOT belong to someone?

The word "unowned" exists, but it usually means "not owned by anybody" as opposed to "not owned by a particular person".

So "This bike is unowned by me" is possible, but unusual. "A sale of unowned property" is perhaps more likely.

In some software systems, items may have owners (whatever that might mean in that system), and we could talk about an "unowned item" there.