You rarely see true foreign correspondents anymore. There are reporters covering foreign news, yes, but there are fewer and fewer who actually live in the region their covering, working in their organization's foreign bureau.
During times of war, you see them. But most of the time these are reporters who were sent to the region specifically because of the war. They are there on assignment, like any other reporter, and when the war is over (or pretty much over) they are flown back home or onto other international assignments. War is the driving factor of foreign correspondence today, it guarantees that news will be generated in that region and that it will need to be covered. There will be a number of different stories and angles as well, aside from just covering the battles and troop movements. There are people whose lives have been turned upside down and are being affected because of the area they live. But there are only so many of those stories, and eventually the public will grow bored and there will be no more need for a large number of reporters to tell those stories.
Traditionally, foreign correspondents would live and cover the area they lived in for years. They would know the language and the people, which would make gaining access for stories easier. But more and more papers have shut down their foreign bureaus and those who are left are responsible for covering a larger region than before. When news happens immediately in a region where there are no foreign correspondents nearby, they rely on the news from international organizations or local reporters, or freelancers if they have decided to come fill the gap for coverage of the region that they see in the international news.
Whenever I would talk to editors or professors and say I wanted to become a foreign correspondent after I graduated, most of them would say, "Wow, we never hear anyone say that anymore. Good luck with that." The nature of how we get our foreign news has changed, we rely more on the one organization that may have a reporter left in the area or freelancers who are willing to brave the unpredictable environment. But it has definitely changed and it seems unlikely that it will go back to what it used to be. The heyday of foreign correspondence has ended, for better or for worse, and most of the time it's definitely not for the better.