Foldback
A foldback, also known as folding under or a foldback underneath, is a situation in which a ladder changes direction and turns into a ladder closer to the edge. The attacker is still in control after the foldback. A foldback is not to be confused with a switchback, in which the ladder changes direction and continues further from the edge.
Foldbacks are only possible from 4th row ladders or higher, as there is not enough space under a 3rd row ladder to fold back.
Examples
D5 foldback
Suppose Red has a 4th row ladder approaching a red stone at d5 (or the equivalent cell on the opposite side of the board):
In this situation, the stone on the 5th row does not act as a ladder escape. For example, Blue can block the ladder as follows:
However, Red can now get a foldback, namely a 2nd row ladder from right to left:
If Red has some way of escaping this ladder, Red connects.
C4 foldback
Similarly, consider a single red stone at c4 (or the equivalent cell on the opposite side of the board).
This stone can serve as a 4th-to-2nd row foldback, even in situations, such as the one shown here, where it would not normally escape a 4th row ladder.
Note that Blue cannot yield, because then Red gets a 3rd row ladder, which the 4th row stone does escape.
A3+A5 foldback
Consider red stones at a3 and a5 (or the equivalent cells on the opposite side of the board).
Red can use this to get a foldback from the 4th to the 2nd row:
If Blue plays somewhere other than 4 or 6 (in either order), Red connects outright.
Moreover, Red can also use this to get a foldback from the 5th to the 3rd row:
The same two stones can even be used for a 6th-to-4th row foldback:
Foldback threat
We say that a ladder carries a foldback threat if getting a foldback would allow the attacker to connect. Even if the attacker cannot actually get the foldback, the mere threat of a foldback can be an advantage for the attacker. An example is the 4th-to-6th row switchback using A4, which only works in the presence of a foldback threat.