This theory refers to the possibility that Dumbledore knew that his death was inevitable at the end of the sixth year and that Snape would be the bringer of it. Our other theories broach this theory somewhat, at least mentioning that Dumbledore knew that he had to die, but I believe there is concrete evidence of this early on in "Half-Blood Prince," and this evidence is Snape being appointed teacher for the Defense Against the Dark Arts position.
For the first five years that we were exposed to Snape, he has always been the Potions teacher. Then, all of a sudden, in Harry's sixth year, Snape is the DADA teacher. Why, I wonder, would Dumbledore hold off this position for five years and then all of a sudden give it up? The answer lies in his vast knowledge of past, present, and future (not so much "seeing" the future more so being aware of it).
He knew that Snape was a former Death Eater and was a spy for the Light. He knew that he was aging, therefore directly causing slower reflexes and weaker defenses. He knew that Voldemort was back and that the Wizarding world was at war. He knew that Snape would inevitably be called to service. All of these are indications that Dumbledore had that would be key in his own death.
Both Dumbledore and Snape knew that by the latter taking part in the former's death, Snape would never be able to return to Hogwarts (either because he was not allowed, or because Hogwarts was not reopened for parental assurance). If Snape was forced to do the unthinkable {kill Dumbledore}, before he was to become DADA teacher, then his dream would be unfulfilled. Being the DADA teacher was the one thing that Snape desired, and by killing Dumbledore before he got the post, the position would remain only his desire, never his reality, and two injustices would have been done.
Dumbledore knew how much this post meant to Snape and to just all of a sudden give him the position after waiting five years shows that he must have had an indiction or clue that his death was approaching and that Snape would be involved in it, his involvement being the act of following his duties as a Death Eater while keeping his cover as a spy safe.
To sum it up, Dumbledore somehow knew it was coming.
