Looking at maps of the Maurya Empire, it seems like they never conquered the southern tip of India (or Sri Lanka). Why?
Two reasons:
By the time the Mauryans had reached far south enough to have a border with the Tamilkam states, Ashoka had already converted to Buddhism. So for religious reasons, he did not want to wage any more wars.
The Tamilkam states and Sri Lanka were effectively all vassals of the Mauryans. So even if Ashoka had never converted, I'm not sure that he would have bothered to conquer them anyway. There was just no need.