Dead Button Rule

"The big blind is posted by the player due for it, and the small blind and button are positioned accordingly, even if this means the small blind or the button is placed in front of an empty seat, giving the same player the privilege of last action on consecutive hands." (from Robert's Rules of Poker)

If the small blind busts out and is not replaced by a player from another table, the button moves to the now empty seat (the seat vacated by the eliminated small blind). The player who was the big blind now posts the small blind and the player to his left posts the big blind. Since the button is now located at an empty seat, the player who was the button will, in effect, be the button once again.

Dead Button Rule - Small Blind Busts Out
Hand	Seat 1	Seat 2	Seat 3	Seat 4	Seat 5
1	B	SB	BB
2		B (x)	SB	BB
3		(x)	B	SB	BB

If the big blind busts out and is not replaced by a player from another table, the button moves to the player who was the small blind and the player to the left of the eliminated big blind posts the big blind. There is no small blind for that hand. On the following deal, the button moves to the now empty seat (the seat vacated by the eliminated big blind player) and the two players to the left post the normal blinds. Since the button is now located at an empty seat, the player who was the original small blind will, in effect, be the button once again.

Dead Button Rule - Big Blind Busts Out
Hand	Seat 1	Seat 2	Seat 3	Seat 4	Seat 5
1	B	SB	BB
2		B	(x)	BB
3			B (x)	SB	BB

If both blinds bust out and are not replaced, the same player will be the button three hands in a row. The button moves to the now empty seat (the seat vacated by the eliminated small blind player) and the player to the left of the eliminated big blind posts the big blind. There is no small blind for that hand. On the following deal, the button moves to the next empty seat (the seat vacated by the eliminated big blind player) and the two players to the left post the normal blinds.