The end dancer does a Cross Fold to face the center dancer in the other half of the wave.
But the center dancer won't be there by then, because the center dancer will have started moving also. The center dancer starts by doing a Fold behind the adjacent end dancer. But that end dancer will already be gone.
The original center dancer continues by following the end dancer and continuing to turn, and takes hands with the end dancer to form a couple.
Note that at the beginning of the action both the end dancer and the center dancer start turning toward the hand-hold that they have with each other. From a right-handed wave, everybody will start by turning to the right. They can help each other get started turning in the correct direction by giving a slight tug on each other. But the end dancer should not try to "drag" the center dancer around. Each dancer is responsible for doing their own part.
From a left-handed wave, the actions are the same except that everybody will start turning to the left.
Note that the original center dancer actually turns all the way around (360 degrees) by the time the action is over. The end dancer only turns around halfway (180 degrees). The end and adjacent center must drop hands as they start to turn. They can take hands again, as a couple, as soon as they get to the point that they are both turning to face in approximately the same direction, toward the other couple.