I'll expand a bit.
What I found out is the timekeepers use a second clock in case of errors. For example there's time when the player's movement is the cue for the time clock to start (eg a kick-in) so the player might go but then the umpire blows the whistle and calls them back because of the position on the mark or the other footy is on the ground or whatever so the clock has ticked a couple of false seconds.
When that happens they don't add the time back on to the main clock (the TV one) but keep a second clock which they 'add' the missed time back on at the next opportunity, which is a stoppage.
So if there was an instance of that and the siren came before a chance to add it back on, they would let the siren go for those extra seconds. A very rare circumstance but quite possible.