A player's string is capturable-2 if
- it is neither uncapturable nor capturable-1 and
- the opponent cannot force capture of the string's stones and prevent a local-2 permanent-stone of the player.
Examples are rare but here is an example:
The marked stone is capturable-2.
Note that it is not capturable-1: if White captures it, Black can try to play a local-1 stone. However, White prevents this by playing on the intersection of the marked stone. Afterwards, Black playing there fills one of his own eyes so White captures the whole black group and then Black cannot establish a permanent-stone on the intersection of the marked stone.