My anwer is mostly based on the speculation that <PERSON> intended to make the Elder Wand into a trap for <PERSON>
The complete thread is here http://scifi.stackexchange.com/questions/73717/why-didnt-severus-disapparate-in-the-shrieking-shack
from deathly Hollows chapter: King's Cross
“But you expected him to go after the wand?”
“I have been sure that he would try, ever since your wand beat <PERSON>’s in the graveyard of Little Hangleton. At first, he was afraid that you had conquered him by superior skill. Once he had kidnapped <PERSON>, however, he discovered the existence of the twin cores.
...naturally set out to find the one wand that, they said, would beat any other.
...He believes that the Elder Wand removes his last weakness and makes him truly invincible. Poor <PERSON> . . .”
Now that <PERSON> is sure that <PERSON> was after his wand. <PERSON> forms his plan. <PERSON> intends to turn the Elder wand (Unbeatable wand) into a trap for <PERSON>
The first step is to have <PERSON> kill him, in such a way that wand ownership does not transfer to <PERSON> (<PERSON> intends to die unvanquished)
Second Step is <PERSON> forms his plan with these scenarios in mind
Scenario 1
<PERSON> steals the wand from <PERSON>'s grave (thinking and "believing" that stealing the wand will be enough to make him the wand's master).
* end results:
* <PERSON> would "not" have to die (preferable outcome - in <PERSON>'s mind).
* <PERSON> won't order anybody else to kill <PERSON>. <PERSON> "believes" that he owns the Unbeatable Wand and <PERSON> himself will want to kill <PERSON> (which is the essential part of <PERSON>'s plan).
Deathly Hollows chapter the prince's tale
“So the boy . 773
. . the boy must die?” asked <PERSON> quite calmly.
“And <PERSON> himself must do it, <PERSON>. That is essential.”
Scenario 2
<PERSON> steals the wand "but" eventually deduces that he needs to kill <PERSON> (<PERSON>'s killer) to gain the Unbeatable Wand's loyalty.
* end results:
* <PERSON> has to die (regrettable to <PERSON>'s mind of course, but necessary)
* <PERSON> won't order anybody else to kill <PERSON>. <PERSON> "believes" that he owns the Unbeatable Wand and <PERSON> himself will want to kill <PERSON> (which is the essential part of <PERSON>'s plan)
To resolve the discrepancy of wand ownership:
Deathly Hallows chapter the Flaw in the plan
“He killed —”
“Aren’t you listening? <PERSON> never beat <PERSON>! <PERSON>’s death was planned between them! <PERSON> intended to die undefeated, the wand’s last true master! If all had gone as planned, the wand’s power would have died with him, because it had never been won from him!”
.
Deathly Hallows chapter King's Cross
He believes that the Elder Wand removes his last weakness and makes him truly invincible. Poor <PERSON> . . .”
“If you planned your death with <PERSON>, you meant him to end up with the Elder Wand, didn’t you?”
“I admit that was my intention,” said <PERSON>, “but it did not work as I intended, did it?”
“No,” said <PERSON>. “That bit didn’t work out.”
First quote takes precedence since it is more specific.
The conversation between <PERSON> and <PERSON> should actually be read as
“If you planned your death with <PERSON>, you meant him (<PERSON>) to end up with the Elder Wand, didn’t you?”
My speculation is that it was only in King's Cross chapter that <PERSON> realized that <PERSON> was supposed to end up with the wand. <PERSON> also needed to confirm this with <PERSON> since only <PERSON> has the complete specifics of his own plan. 773