Two-space notchers not fully connected
So long as a is not occupied by White, Black can live (provided Black plays first). The vital point is at b.
Black has to be careful in responding to the hane at . Only playing at will live. Playing at a is wrong.
Playing at is wrong. White makes a placement tesuji at , causing an exchange at , followed by connecting at . Black faces a shortage of liberties - being unable to play at a - and dies because the eye on top cannot be formed.
The descent at is incorrect as well. White can kill the group with a hane at (aiming to capture two black stones at a), followed by a placement at . attempts to divide the space to make two eyes, but the connection at leaves Black with a shortage of liberties, and Black cannot play at b to defend the second eye.
If White starts at b, Black's 222WN notcher dies (2 and 3 are miai). Either hane (5 or the other one) kills as well (White gets the second hane or nakade). White can also kill from outside by filling (222WW).
Starting with 2 would let Black live (with 1). Therefore fails if is one to the right (222NN), but hane still kills. Actually hane kills any 222xy.
If the lower leg is longer (223WN), White can not kill (hane is met with 1, and 1 with 2). Neither if the upper leg is longer (223NW, similar).