Many devices require a power supply to operate. If your device is powered via Power over Ethernet (PoE), your phone service will not be interrupted unless your router is also down. In that case, your internet connection will be unavailable.
However, you can still stay connected by using a device with an independent internet connection, such as your mobile phone with a VoIP application. Alternatively, you can activate call forwarding to another number in order to temporarily handle your incoming calls.