Has there ever been a major conflict where the two (or more) sides have beat each other up so badly that another group steps in and takes over with relative ease. This can be anytime in history and can deal with a country or some territory.
An example: ( If Russia hadn`t been involved in WWII…) Much of Europe had been embroiled in war and would have been millitarily decimated to the point that Russia could have taken over several countries of their choice. Maybe?
Maybe a bit off from your requirements, but the Arab revolt during World war one is maybe close.
The allies used arabic forces as part of their war against Turkey. But as Damascus fell to the allies, the Arabic army took and heald Damascus for themselves. (this btw is from the Seven Pillars of Wisdom, accounting Laurence of Arabia and the Arab revolt). Though the Aliies were still strong enough that they could have taken Damascus from the Arab army, to do so would have been a political disaster. So the Arabs gained control of their own city through exploiting the war between the Allies and the Turks.
England, 1066. Two armies waited to set sail to conquer England, ruled (mostly) by a newly installed king of questionable authority, Harold Godwinson. Harald Hardrada, king of Norway and Top Viking of All Time waits in the Orkneys. William the Bastard waits in Normandy. The winds blow south. Hardald H. goes first. Makes a bad strategic decision and dies at Stamford bridge. Meanwhile, the wind had changed, William’s turn. He had already landed.
The English army has to march south without rest. They were just barely defeated at Hastings. William the Bastard became William the Conqueror.
If the wind had first blown north in late September of 1066, the history of England would have been quite different.
I suppose you could argue that the break-up of the European colonial empires following WWII was an example of what you’re looking for. If the British, French, Belgians, and Dutch hadn’t had to fight the Germans and Japanese, they probably could have held on to their colonies. Pointedly, the Portuguese, who stayed out of WWII, held on to their empire the longest.
Didn’t we take advantage of England being tied up with Napoleon to fight the War of 1812? Dunno if the results are what the OP was asking for, but it follows the general idea.
Why exactly did the Romans say, “Divide and conquer”? And didn’t the British and other colonial powers take advantage of others’ problems?