It waits. It is very patient, though whether that was innate or something it had to learn is uncertain. There is not much for it to do. Not yet, anyway. It is not a point; a point is a mere dot, a marker. A point is not the end.
Lines extend infinitely, of course. No one questions that. That's not the issue here. But even infinity has bounds. There is always a larger infinity, a set tat contains the set that contains the set. Eventually, they have to hit the edge, to converge.
When they do, it will be waiting.