you memorize not only what piece. But what sticker you have on that piece. Then when you solve it, you'll get the next piece and the sticker that was in the location of the sticker you just solved.
If you solve the buffer edge. Then you'll have to shoot that corner out to another location, starting a new cycle at an unsolved location. When you'd normally do a dbl corner swap, or start a new cycle by just rotating the cube, 2-cyclist must do as stated above. That is our means of starting a new cycle on the corners. I personally orient corners that are permuted, however disoriented w/ two 2-cycles. I could use orientaition algs, which could be faster ... but who knows.
I'm stepping up my game ... learning 3 new 2-cycles and a 3-cycle system as well.
Later,
Daniel Beyer