During a power outage, why do some landline phones still work?

What is the basic science behind the landline phone?

It seems that it would be our only means of long distance communication in the event of a nationwide power outage.

It's based on 48 V source at the central office. May or may not be battery based now, but used to be wet cells. Carbon microphones and a speaker.

There is a transformer called a hybrid transformer that provides cancelation of most of what you speak in the microphone.

Pulse dialing interrupted the line to dial. Before that operators were used. Now it's been replaced with DTMF (2 different simultaneous tones for each digit).

The ring generator was a hand crank thing that generated about 85 V AC voltage at 20 Hz.

Any phone that plugs into AC power won't work when there is a power failure. Verizon FIOS puts a rechargeable battery at your house when they deliver telephone via fiber.

For landline phones the telephone company has their own emergency backup power in case the commercial power goes out. This backup power is a combination of batteries and diesel generator at the central office, or just batteries for lines that run through multiplexers in the field. For landlines the power to operate your phone comes through the wires from the TelCo into your handset. Obviously if you have a telephone that requires its own source of electricity (like a cordless phone) it will not work in a power outage. You are right in that in case of extended outages landlines are probably more reliable than cell phones or VoIP (i.e, phones that run through your cable TV line).

Here is an article on how phones work:

Howstuffworks "How Telephones Work"

Here is something for Cordless phones during outages to maintain communication:
PROVANTAGE: CyberPower Systems CPS180PHV Phone Saver - Cordless Phone Battery Back-up System
A UPS would also work fine.
I know people who only have Cordless and are without communications during a power outage.

Strat:

That's an interesting UPS. I have a cordless system, a high intesnsity light and a PERS alarm on a 120 V UPS. The UPS was free, but it cost me $20 for a battery.