A phone is for communicating, so finding other options for communications would be logical.

If cell towers are overloaded or down in some incident, but you can still find a WiFi signal, then you can still call or text or even video chat with people with apps like Skype. Pay a little extra and you can dial out to other phones or have a virtual phone number that people can ring you up on (although you're consuming your battery waiting for a call).

And for lots of people, other media such as Facebook and Twitter have replaced voice calls and text messages.

Often, it's just that initial, "Are you OK? Are the kids OK?" that is most important to a person. After that, if you're out of touch, it's not so bad psychologically and you can just carry on.