Your internet service needs the fiber network and electricity to work. Your town's network has invested in a back up generator to keep the internet working even if power is out in town but you will still need a source of power at your home to use your internet and phone service including 911.
There are three devices which will all need power to keep things working during an outage:
The ONT (generally in the basement)
The router (often on the first floor)
The Telo device and your phones
You should plan for these devices to be on a circuit which is served by your generator or power them each with a battery back up or uninterrupted power source (UPS) available online or at local big box stores.
In the event that the internet is down (either the drop to your home or a larger scale outage), you will not have phone or 911 service until it is restored.