In Lightning Returns: Final Fantasy 13 there is a pre-determined number of monsters of each type in the game. If you spend your time and kill them all, either on purpose or by accident, you can end up wiping out the whole species. This is according to a Famitsu interview with Game Design Director Yuji Abe and Battle Design Director Nobuyuki Matsuoka.
However, when a player encounters the titled Last One of a given species, it will be much tougher than the rest of its kind and may drop a rare piece of loot. In addition, they revealed that once you complete the game, it will unlock a hard difficulty. This mode will have harder monsters that will drop higher level loot.
Lightning Returns: Final Fantasy 13 will come out for the PlayStation 3 and others in February of next year.