Area power cuts or no phone signal
If you have a phone connected to your router, if there is a power cut, it will no longer work unless you have a backup power supply. If the area affected by the power cut affects mobile phone towers, then you will also be unable to make a mobile phone call. The only way you can then communicate with the outside world is by a satellite phone. These are big and expensive. However, in the near future you will be able to use an ordinary mobile phone to make calls by satellite, where there is no phone mast in range.
https://www.vodafone.co.uk/newscentre/smart-living/everything-you-need-to-know-about/direct-to-smartphone-satellite-service-everything-you-need-to-know/