This page discusses the fact that under Japanese rules, a group which is surrounded by a live enemy group and whose eyeshape can be reduced to bent four in the corner is dead.
Let's talk over this position from bent four in the corner.
By Japanese rules the white group in the above diagram is considered dead and is removed without playing any ko. The reason for this is as follows.
Since White can never play a nor b, Black could fill all outside liberties after play has stopped at the end of the game, and then play a to create the ko explained in bent four in the corner and shown in the following diagram:
The rule is now that in the determination of life and death at the end of the game, after play has stopped, the only ko-threat for a ko is a pass for that ko. If White makes such a pass, Black wins the ko, anyway.
The first written Japanese rules, in 1949, also ruled that "bent four in the corner is dead". This ruling has been discussed ever since, because the fact that some (even many)[1] games contain unremovable ko threats makes this rule unfair towards the defending side in this position.
Under Chinese rules or under rulesets where life and death have to be proven rather than simply decided, the ko should be played, because unremovable ko threats can make a difference.
When the surrounding group of a group which is supposed to be dead by this rule is not alive with two eyes itself, the rule doesn't apply: in that case the aforementioned ko will be played out. [2]
See also
Authors
[1] Many games in number, but a tiny fraction of all games.
[2] Well, it can be more complicated than that too, but I think I'll leave that for some other Robert.