The established name for this shape is 1-eye-flaw, but I dislike this name, so instead I’ll call it…
Frozen life
White has just captured at A1 - black cannot recapture at A2 due to ko.
The other moves are suicide/self-atari for black, so passing is the best option.
Similarly for white: filling at A2 would be suicidal, so white passes.
Thus the game ends here: the one-eyed white group is alive with 7 points!
I think “Frozen life” is descriptive, because the group is only alive as long as the game remains frozen in this state: if it was possible to unfreeze the game by making a non-passing move elsewhere on the board, white would die.
It may seem like the reason for this strange result is only the fact that the game immediately ends after two passes, but even if black were allowed to dispute the result after two passes, superko would still forbid him from capturing at A2, so there really is no way to kill the group.
Here I should mention that in some rulesets, passing lifts some or all ko-bans. This is not the case in Tromp-Taylor rules, and I believe not in Chinese, AGA/BGA or NZ rules either. So under all these rulesets, the white group lives.
(NZ rules use situational superko, but the distinction does not matter in this case)
(also Chinese rules in practice are different from Chinese rules in theory, which is why Tromp-Taylor rules is my go-to ruleset for this thread)
Ok, so with all of that boring rules stuff out of the way, what fun things can we do with this weird and wonderful way to live?
Consider this position, with a frozen life in the top left:
If the game ends here, black is losing by 1 point. Can black do better?
Yes! Black should fill an eye with F2 (or G1, it doesn’t matter), to unfreeze the game:
Black voluntarily dies in gote with the lower right group! Regardless of whether white passes or captures on the next move, the position has changed, so black can now freely capture at C7 and then at B6 on the move after that.
Since the upper left group is slightly bigger than the lower right, this exchange swings the game in black’s favor: the final result is B+1.
Next consider this position:
Here the top left is smaller than the bottom right, so it’s not in white’s interest to die in gote at F2.
Instead, white should suicide at A1! After that the upper left group can be killed without problems.
If suicide is not legal, then the upper left group and white’s chain of four stones are both alive!
Black never wants to capture the four stones, since then he loses the frozen group.
In summary, not only can one-eyed groups live, unconditionally pass-alive groups can die! And if suicide is illegal, we can get big chains in atari, surrounded by solidly alive groups, but which are nonetheless alive!
Personally I think this is lovely, but if you find it ugly, don’t worry - the chances of a frozen life happening in a real game on a 19x19 board are practically 0 