Today I want to share two examples of groups that look dead but aren’t. For dramatic effect, let’s name them:
Zombie groups
Let’s start with this position, which we’ve discussed here on the forums before:
@yebellz did an excellent analysis here, so I’ll just redirect you there rather than redoing the work myself! 
The quick summary is that although the white group on the left is locally dead, it’s not in black’s interest to kill it, because doing so would give white a ko threat, enabling her to start and win the E4 ko. Therefore the white group is globally alive in seki.
Such small-board examples are often completely constructed and would never happen with reasonable play from an empty board. But this position actually comes from near-perfect play! Only 5 and 7 are not optimal in this sequence:
Source: Solving Go for Rectangular Boards (section 5.2)
A few weeks ago, this Lifein19x19 post by Gérard Taille brought to my attention an even more shocking version of this phenomenon.
Surely the top left group is dead! It only has one eye, and it’s surrounded by an unconditionally alive group. Even with arbitrarily many moves in a row, black can’t live.
But, just like in the previous example, an issue arises when white actually tries to take the group of the board. After white has played two more moves inside, black can capture as a ko threat! Therefore black will choose that exact time to start the ko in the upper right:
When black makes the ko threat at 6, white is forced to choose between killing the left and staying alive on the right. The right group is bigger, so correct play is to finish the ko with 7, and let black live on the left:
Now here is where this example differs a bit from the previous one: white should play out this sequence at the end of the game! If she instead leaves the original position as seki (just adding a stone at B6 for an extra point) the score is W+3. But in the final diagram above, the score is W+6.
If you’d like to make the sequence above necessary to win, just imagine that C1 and D1 are black stones - I’m too lazy to change the diagrams
In conclusion, with correct play the obviously dead black group comes back to life!
Note that it’s not too far-fetched for this to happen in a real game. Unlike the frozen life in my previous post, this has nothing to do with super-ko, and it doesn’t matter if both sides have lots of territory-filling moves available. We just need these ingredients:
- A black dead group where white capturing it will create a ko-threat. This is true of many nakade-shapes.
- Some shape where black can start a ko at any time, and white can’t remove the ko. The upper right corner from above is not a common shape, but a standard Ten Thousand Year Ko has similar properties and could have the same effect under the right circumstances.
- Black must not have been able to start the ko earlier in the game for a larger profit.
On one hand, it seems likely that black could get some nice profit by starting the ko earlier, since it’s so heavy for white. On the other hand, living with a dead group like we saw above may be even bigger! So if black has such a dead group, and is aware of the implications, he may choose to leave the ko on the board until the final moments of the game.