It depends on the security system and the VoIP provider.
The two most important considerations are the way that your VoIP security system communicates with the monitoring centre, and how the VoIP service gets power.
Old fashioned copper lines get their power from the local exchange who have battery plus back-up generators in order to keep the old phone system working whilst there is a power cut.
With a fibre system the connection is powered by the household supply. Power cuts and the line is dead.
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VOIP? 
VOIP? 