These two green spaces, one beside the Russell House on the east side of the Thomas Cooper Library reflection pool, and the other on the west side of the pool were once USC parking lots. It was almost impossible to find a spot in either lot, but if you could, it was your best shot for actually being able to park "near" to the library.
The parking situation at USC has always been fluid, and it is not unusual for a lot to vanish, but it is unusual for said lot not to be replaced with a building. There used to be a parking lots behind and in front of the Welsh building, for example, but they have all now been built over.
I believe the lot by the Russell House vanished first, perhaps at the time Green Street was closed. I think the west lot lasted a good bit past that. At any rate, if you have checkout privileges at the library, you're going to be be toting those books a couple blocks in most cases!