The saved state is part of the state of the image. During import, it seems to be set to the state of the edit controls just after default processing, that is, if you've set import default development settings, the state after it has done that processing.
You can change the saved state during your development by selecting side-by-side and using the before/after controls available next to the side-by-side control.
It appears to me that there is one saved state for an image and all of its virtual copies. After this discussion, my new work-flow for side-by-side, will be to enter the develop module, select side-by-side, set the saved-state to the current state of the image, then make the necessary edit changes. If continuing on to soft-proof, I will again set the saved state to the current state, and turn on soft proofing. If I come back later to the master image or this or any other virtual copy, outside of soft proof, I will go through the steps to set the saved-state because it may not be apparent which copy the saved state corresponds to. There are lots of permutations possible, most of them are bad news.