1) After there are two possibilities; see below for a different option for Black.
2) After , White may play at . If so, then Black plays at instead. (After , the points and are miai for Black.)
After in the first diagram above, Black can also play here instead. It's unusual that a move at the 1-1 point works! Afterwards:
1) if White b then Black a and Black is alive (if White c then Black d)
2) if White a then Black b as in the main line.
3) if White c then Black d; then a and b are miai for Black to live.