Cornersoul: So what happens to all the dementors where will they go will they be destroyed if so, how
J.K. Rowling: You cannot destroy Dementors, though you can limit their numbers if you eradicate the conditions in which they multiply, ie, despair and degradation.
(from mugglenet.com - scroll down to "J.K. Rowling 'Deathly Hallows' Webchat")
They cannot die, but they can and do breed when the conditions are right.
We've also seen that a group of them together can cause many of the conditions that allow them to breed (Dumbledore forbid them to be on school grounds, as they would have caused this mood across the school).
Does this mean the world's population of Dementors can only increase? If left unchecked in an area, such as a war-torn 3rd world country, could their population increase to the point where they can turn whole countries into places like Azkaban?