If your home line is down and nearby cell stations are not operational, then what? Pigeons? :)
It depends: what is the occasion in which the power grid goes down (or your IP carrier is down) and multiple mobile operators are down?
Let's say: flooding, earthquake, riots, evil government shutting down telcos.
Then there is a high chance that also my land line would be down.
Thinking of it, I must get some homing pigeons _now_ ;)
We have highly redundant communication systems compared to when landlines were the only option and SPOF in the building.