Everyone needs to have a cellphone number, in case of power outages!
If everyone relies on the internet to connect with one another, then if the internet cuts out: people have absolutely no way of directly reaching one another!
How can you fix this problem, in the case of emergent scenarios?
I dont know what exactly are you asking? Cellular service and internet are two competely different technologies.
Cellular service does continue to work when the power goes out. If you are using a laptop you can access the internet by tethering your cellphone to yuour computer. Most cell towers have either a battery back up system or a generator installed to maintain temporary power to the radio equipment.
Internet services operating when the power goes out are based on two issues. First the provider needs to have backup power enabled for their equipment.
For DSL (high speed internet through the phone line), their is power provided to the equipment and in some cases there is not.
For cable internet there needs to be backup power at the office where the signal originates as well as to each individual amplifier connected along the wiring between the hub and your home. Some cable companies offer this others do not.
In addition to power backup from the internet provider there needs to be power backup at each person's home in order to supply power to the modem and the computer.
I studied radio electrons, computer networking, and telecommunications and I used to work for one of the Roger's wireless dealers. (Before I discovered that Telus was much better).