Are we assuming infinite gravity in a single direction? A flat earth then? Or an infinitely diameterical round earth ? Gravity at the current north and south poles of an approx round earth are diametrically opposed so in that circumstance, at some point, you could effectively be lowering the rope up, against gravity. Is that the Indian rope trick?
It would never work, even if the rope was of infinite length............. ...........the end would keep burning away as it tried to reach the end of the infinite hole.....
That the question has an infinite number of correct answers depending on what finite/infinite assumption you choose to make?
Apparently they arrested a man who was loitering near to said hole. When asked to explain the large sum of money found on him, he said that it was "money for old rope".