If Toshiyuki Sakai is accessed while installed, you may swap him with an agenda or asset from HQ. The new agenda or asset is installed unrezzed, and keeps all advancement tokens on Toshiyuki Sakai. The Runner can choose not to access the new card.
For the new Jinteki Executive Toshiyuki Sakai, what happens with a loop of two Toshis? The Corp has Install, advance, adanced a Toshi the previous turn, and the runner makes a run. When the runner accesses Toshi, the corp swaps him for ToshiB from HQ. The runner chooses to access the ToshiB, which is then swapped back for ToshiA. This loop happens a few times. Which player is responsible for ending the loop? The Corp can continually swap the two Toshiyuki Sakais. If the Runner continues to access the Toshiyuki's, and the Corp shows no sign of changing the cards, then a judge can be called over. It could be considered slow play/stalling on the side of the Corp.
The Corp is the one who is making the choice to continue swapping; this choice occurs before the Runner choice of whether or not to access. Therefore, the burden is on the Corp to stop swapping before it is on the Runner to stop accessing.