Here is one I don't get. AT&T recently forced my father tio switch from DSL to Uverse. And that means that his dial tone comes through the Uverse modem. He lives in Houston, they have hurricanes, he loses power, he has no phone service. How can he make a phone call if he loses power.
If you loose power your UVerse system will have at best limited function. And you are correct to be concerned for you father. Without power to Uverse you need to know what limited functions you have.
Don't just blame ATT, Venison FIOS and Comcast Xfinity will also have some limitations. You can read that some of their devices have battery backup. Well I know for a fact that they don't. If they do it is limited to maybe 4 hours.
So I suggest you test your system. Unplug your modem. If you still have dial tone you may be OK for up to 4 hours. Remember you will not have dial tone on any other phone attached to the system unless you supply your own power.
You can get inexpensive UPS (Unitteruptable Power Supply} that will allow you to use these other phones as well as your modem. But test them!
And don't plug other things like lamps and TV's. You need the power for as long as the power is out. Make sure you are prepared.
UPS is a partial answer. Make sure you know the limitations. Ask your provider if you are concerned. And you should be living in our rural area.
No power, no dial tone. UPS is the answer