If you are inside a book and the screensaver comes on and you get out of the screensaver, you go back to the book.
If you are in the home screen and the screensaver comes on and you get out of the screensaver, you go back to the home screen.
That makes it look like it remembers its last place and all it does is exit the screensaver and go back to whatever it was displaying before.
But I went into the screensaver from the search screen and it took a couple of minutes for the screensaver to exit. I played around with it for a bit and every time it took two minutes for the screensaver to exit. I went to the home screen and let the screensaver come on automatically and I exited it and it automatically went to the home screen.
So it doesn't remember its last place, it remembers its last command
and re-executes it, whether it be "Go To Home Screen," "Go to book," or "Search this word." So if your last command took a long time, exiting the screensaver will take a long time as the Kindle re-executes the command (moral of the story try not to let the screensaver come on from the search result screen).
Not that it makes any difference, I just thought it was interesting