Two Eyes Can Die
Beginners may have several misunderstandings regarding eyes and eyespaces. These misunderstandings can lead beginners to believe that it is possible for a group with two eyes to die. Let's explore this:
To be safe from capture, a group of stones needs two irremovable liberties. This is achieved by having two eyes. There are a few, comparatively rare exceptions, such as the situation described by the term two headed dragon.
In the example, the eyes are real eyes of size 1, in which the opponent cannot play (due to lack of liberties, sometimes called the 'suicide rule'). The situation becomes a little more difficult when the eyes are really eye spaces. If the player allows the opponent to play freely inside one of the eyespaces of a group, the status of the group may change.
In this example, Black has played three moves inside of one of the White group's eyes. These moves have removed all but one of the liberties within that eye of the White group. Moreover, they enclose an empty point. This is called an eye in the belly.
The white group is still alive, but it is now tangled up in a seki with the black stones in its belly: if either player plays a, the other will capture the stones linked to it.
Let's take a more extreme example, which may go wrong for beginners.
This White group is considered alive: it has one eye in the corner and a big eye space next to it. Technically, this eye space can be occupied with black stones, in a way that captures all white stones:
However, even with normal, alternating play, it is possible for black to build an unconditionally alive group inside the white enclosure, due to white mistakes in trying to block or kill black. Such a live black group kills the original white stones when it is extended to fill the entire large white enclosure.