The button and SB are determined by the BB. The BB always moves left to the next available player. If the BB busts out on a hand (or leaves the table), the SB is the empty seat on the next hand. Similarly if the SB busts out, the button will be the empty seat, in effect making the same player the button on two consecutive hands.

No player should be allowed to skip the BB, and this is the fairest way to ensure that.