What Exactly Are After-the-Fact Approvals?

The "after-the-fact" approval is an interesting thing. What happens if the boss doesn't "approve" after the proposal went through? If the authority to approve is handed over to someone else in the first place, this system wouldn't need to exist. But if authority isn't handed over, why does this "someone else" have to give approval in the first place?
This is an example of an almost useless two-step approval system.

The above workflow is one that always has to go through two steps for final approval. But the below workflow only goes through two routes in special cases, like when the boss is on holiday.

There are also workflow software products, like Questetra BPM Suite, in which managers can delegate or reallocate tasks flexibly.

• Approval <Two Step>
• Approval <Proxy>