After killing all monsters in an area, encounters still occur, but monsters do not appear. Starting in the Ruins, the protagonist intentionally triggers encounters and kills monsters until encounters with monsters no longer occur this is similar to level-grinding in other RPGs.
The Genocide Route occurs when the protagonist kills every enemy in every region: the Ruins, Snowdin Forest, Waterfall, and Hotland (the CORE is a sub-region of Hotland). Battle text after the protagonist exhausts the kill count.