[pigscantfly]

Other folks may have more apt examples to share, but I would examine the history of Dacia and also the Sasanian fortification lines both east and west (but especially east) of the Caspian Sea -- both of which separated the empire from nomadic tribes of the steppe.

I believe these involved depopulated regions both north and south of the main defensive structures to allow harrying of invading forces while denying access to plundered resources.

Eventually, they were overcome by the Hephthalites (aka White Huns) following heavy Sasanian losses north of the limes in the AD 484 Battle of Herat, but it's interesting to note that the defensive structures separating southern 'civilization' from the steppe were considered a joint responsibility of the predominant (Roman/Sasanian) empires in spite of their generally being at war with each other, as the nomads were a shared threat.

Edit: Another great example is drawn from Caesar's description of Helvetian practices in his Gallic Wars; the Helvetians, a Germanic tribe located in modern Switzerland, had deliberately depopulated a wide area around their territory for defensive purposes.