Obviously it depends on the country and situation but I can refer you to what happened to land between the Polish and German border post-WWII. In that case, German land was claimed by Poland and the German citizens were often forced to relocate. Polish citizens were then given claim to the land. In some cases, the Polish citizens had been ousted from their own homes in the same process because they lived in land now claimed by Ukraine. Here's an article that discusses the historical situation along with a look at more modern terms.

Another example is Lviv. It was a largely Polish city but it was "de-Poled" after WWII.

In the US Mexican War, when Mexico lost the war and a treaty was created because Antonio Lopez de Santa Anna (Mexico's President and Military Chief) decided to do so in order to save his life. The treaty (Guadalupe Hidalgo Treaty), in one of its stipulations an option was given to Mexicans living in the lost land. They had a period of time to decide to either stay and receive US citizenship, or leave to Mexico.