(Term coined by Dieter)
This shape is alive. The best Black can get in one move is a seki in gote by playing at a (see next diagram). White playing there makes six points in gote.
After 1, if Black occupies two of the four marked points, White should occupy the other two.
1. Black's threat
If Black plays 1, he threatens to kill the group. If White does nothing ...
Black 1 (or any of the other two marked points) sets up a killing shape. The other two marked points are then miai for the kill. If White does nothing at all, Black will eventually be able to almost fill the eyespace with a rabbitty six. If White plays one of the marked points, Black takes the other. The kill then branches into a farmer's hat almost fill or a bulky five almost fill.
So, White answers at 2. Black can either continue at 3 (because otherwise his ko threat loses points: White 3 makes seven points) or leave it as another ko threat (depending on the value of the ko). In either case, White must respond at 4 for the same reason as explained above. The final seki position is reached. Black has yet another ko threat but that is one definitely losing points: White will capture and live with a bent four and 8 points.
2. White's threat
White's threat is certainly less valuable. If Black ignores it, White 3 makes 6 points. If Black answers ...
... meaning this threat is even too large to bear, White 3 and Black 4 follow in the same logic.
Conclusion: It is very unlikely that the group gets killed as a result of a ko elsewhere. Black's first move inside the eye space indicates that the endgame stage is reached where the most valuable moves are about six points. It is unlikely that later a ko will develop whose value is large enough to sacrifice the white group. Of course you never know with amateurs ...