Tourney: Question about player being blinded out and BB raise

[JerseyDP]

Hi, got a question that I was arguing with a couple of friends about.
Home Tourney, blinds at 1k-2K level, Big blind has 2k but has left the game and is not coming back, we have been blinding him out for a few rounds.

As stated BB has 2k with 1-2k blinds. Action folds around to button, who goes all in for about 8k. SB folds.

Now, does button automatically win the hand or do we proceed with both the button and BB flipped up and the had run with the BB winning if he has a better hand,even if he is not there?

If you could provide a link or section of Robert's rules that defines this, it would be awesome. Also, there was some argument of live vs. online poker and that there might be difference. If there is a difference, can anyone point that out?

Thanks for your help.
-DP