Moves like that aren't the most common things in the world, but not terribly rare either. At BNSF we even give them their own symbol -- "B" trains, for "Bare Table"
Usually this happens on a full-train scale only when the cars are going into or out of storage or perhaps for some sort of program maintenance. The economics on intermodal are very tight and pretty much requires loaded moves in both directions. Moving empty trains around is a surefire way to remove any profit that one happens to be making.
As for how lease fleets are 'dealt with' when empty, it's really not any different than any other car because, odds are that someone is presently leasing it and it would go back to them just the same as a car that they actually owned outright. If someone's not, it'll go back to the lessor, who usually has someplace designated to 'park' the cars somewhere and they'll arrange for it to be moved to that location and then pay per diem to whomever owns the track that the car is parked on.