It doesn’t really have anything to do with what the blinds are. When you get deep in a tournament, players generally know which hands they are going to play and which ones they aren’t. This doesn’t affect play much as the lack of the small blind at this point in the tournament is unlikely to change anyone’s strategy. If a player is moved into a dead button seat between hands, he will get to play his next hand as the cutoff. If any other player in the tournament is eliminated, it should not affect the way blinds are posted. If the small blind busts out, the button moves to the empty seat and blinds are posted like normal.
On the next hand, the button moves to the empty seat where the player who busted was sitting, and the small blind and big blind are posted like normal. The player to the left of the button posts posts the big blind, and there is no small blind. If the big blind busts out, the button moves to the player who posted the small blind. If the player is UTG (under the gun), the blinds will not be affected by the player’s elimination. Those different scenarios are listed below.
Depending on where the person was sitting, a few different things can happen.