Whether using the Dead Button or Moving Button, the idea is that every player must pay both blinds, and get an opportunity to be the button, on every orbit.
Do not confuse moving the dead button to an empty seat with the Moving Button rule. In the Moving Button rule, players cannot be the button more than once per orbit, but it comes with the unusual conditions that sometimes there will be more than one big or small blind. It is because that rule is so confusing that most rooms use the Dead Button rule.
With the Dead Button rule, if the SB is eliminated, the physical button can either stay put or move to the empty seat. Either way, the prior button player gets to act last.
Some rooms favor moving the physical button to the empty seat, because that helps the dealer remember where the button and blinds are.
Therefore, in the above example, the physical button will move to seat 2 and the new players in seat 3 and 4 must wait till the next hand, when seat 5 is the button.
But it makes me think of a new scenario:
Seat 1 is the button.
Seat 2 is SB.
Seat 3 is BB.
During the hand, seat 3 is eliminated. The next hand seat 2 is the Button, and seat 4 is BB with no SB.
During this new hand, seat 3 gets filled.
On the next hand, the blinds are seats 4 & 5. As stated above, the physical button can move to seat 3. If so, can seat 3 play? After all, seat 2 already had his opportunity to be the button. The pub league I deal for uses this rule. After all, its just a friendly free poker league.
But in a casino, can seat 3 play? Does it matter if we're talking about a tournament vs a broken cash game?