Alarm panels have a rechargeable battery inside, which will power the alarm in the event of power failure. The capacity of this battery is selected by the installer so it is capable of powering the panel and all devices connected to it for a certain time, which would be at least 24 hours.If someone was to pull the main fuse outside his property that they could just break in without alarming the neighbours because alarms should never go off when the power is removed?
The external siren also has it's own battery inside.
If the alarm is not set, a power failure will have no effect, other than a warning being shown on the panel.
If the alarm is set, power failure won't do anything either, but if someone then breaks in, the alarm will sound in the usual way, as it is being powered from the battery.
If someone cuts the cables to the external siren, it will sound using it's own internal battery, as it requires continuous power from the panel both to charge it's own battery and indicate that the panel is still connected.
If the internal panel battery is ruined, not charged or not installed, power failure will cause the external siren to operate, as there is no signal from the panel.
The internal battery and external siren module need to be replaced at certain intervals, which is why all those people with alarms that blare off every time there is a minor power issue clearly haven't had it serviced or maintained since it was installed.