that idea comes from art of war

Yep, from Sun Tzu's Art of War:

"When you surround an army, leave an outlet free. Do not press a desperate foe too hard."

-- http://classics.mit.edu/Tzu/artwar.html

I think this is also the first time I've heard it quoted in an appropriate context, as opposed to business blabla.

To quote coolsubmission on reddit:

This does not mean that the enemy is to be allowed to escape. The object, as Tu Mu puts it, is "to make him believe that there is a road to safety, and thus prevent his fighting with the courage of despair." Tu Mu adds pleasantly: "After that, you may crush him."

Also comes up in discussing the types of ground. "Death" or "desperate" ground is where you fight at all costs, since otherwise the cost is death.

unless you get saved by eagles

You must not follow the Syrian Civil War very closely!