"Hardline" is a very rare term referring to the fact that the phone is a landline. Most people wouldn't understand it.. It's called a "hardline" phone because the line of the phone is fixed, unlike that of a mobile phone. Hence, the line is "hard", or somehow someone managed to see the connection. "Landline" is a much clearer term.
In context of the text you gave, the speaker is saying that the old lady, uses a cordless phone. But she doesn't know that it is actually a cordless and a landline, which meant that when the garage slid into the Batavia, the line was probably broken and she would have lost contact with the world, as her telephone no longer works.
It seems that "Hardline" was a popular term originally:
But, perhaps Google Ngrams isn't really too reliable, although it does provide some fact.