I am not sure I understand your question. Could you rephrase it?
Assuming you have a phone modem (MTA), the modem takes coaxial signal from Cox and turns it into a signal that you can get via a phone jack on the back of the modem. Some phone modems have battery backups, but this only supplies the modem power, not your phones or the Cox network out on the poles. Most areas will have battery backups on the poles, which are reinforced with generators if the power outage is long. However, how these systems work in different areas is a bit more complicated. See this thread for more info.