Emigration
Some politician or another is always upset about immigration. Emigration is the other side of that electrically charged coin. All those people trying to immigrate into your country are emigrating from another country.
This happens all the time on a small scale. People emigrating from the U.S. to Canada for better access to moose...people emigrating from Germany to France for better cheese. Occasionally, it happens on a mass scale; think: refugees escaping a failed regime.
A famous historical example comes from Ireland during the potato famine, which started in 1845. Things got so bad that, over the next decade, an estimated 1.5 million people emigrated from the country (mostly bound for NYC and Boston). This represented something like 17% of the total pre-famine population of Ireland.