While it's often something of a surprise when you finally do get the axe, you usually have a sense of impending doom, and a feeling that bad things are going down, before it happens. Projects stop getting traction. Upper management stops caring as much about what you're working on. Everyone becomes very apathetic. You get a rash of invites on LinkedIn, and people start updating their resumes.
So, it's rarely a complete surprise, and people often already have some idea of where they're going to go, or are ready to start looking.