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.
Further elaboration: a question of ko threats
1. Black's threat
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 pyramid four 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 ...