Typically the 12th house is the considered the house of residence in a foreign country. The 1st house represents the place of our birth, and the 12th house from any house represents the loss of the indications of that house. Therefore, the 12th house is the loss of one's birth place and therefore residence abroad. It can also simply mean travel to foreign places and not necessarily settling down.
In addition, the 7th house is also sometimes listed in texts as a house of foreign travel or residence abroad. For instance, the Sarvarth Chintamani refers to the dashas of planets located in the 7th house as a time of travel or residence abroad. For instance, it says:
"During the ruling period of Jupiter in the 7th house, the native gets wife, wealth, son, happiness, goes abroad, is victorious in battle."
Likewise, it later says the same for a Rahu dasha:
"During the ruling period of Rahu located in the 7th house, the native soon gets destruction of his wife, goes abroad, suffers losses in agriculture etc."
Why is the 7th house a house of foreign residence? Usually it's just considered the house of relationship. The reason is because the 7th house is the farther house from the 1st house, being the opposite house. The placement in the sky of the 1st house is on the Eastern horizon, while the 7th house is on the Western horizon. Therefore, the 7th house is the furthest from one's birth place or a foreign location.
This all makes logical sense, but there may still be some lingering doubt that the dasha of a planet in the 7th house could actually result in residence abroad. Therefore, here's a chart of a woman who was born in Hong Kong, and when she was 10 years old her family decided to move to the USA. This was during her Mercury-Rahu dasha.
Notice that Rahu is placed in the 7th house, and Mercury is the 4th lord, and in the 4th house from the Moon. The 4th house is of course the house of home, indicating events related to home in her Mercury dasha. Notice how Rahu is also placed in the lagna of the chaturtamsha chart (D4) the divisional chart for home, indicating a significant event related to home in a Rahu dasha. At the time of the move, Rahu was transiting through her 12th house, Taurus. Furthermore, Rahu is the planet of foreign connections. All these factors show a repeated pattern indicating a major move to a foreign country in her Mercury-Rahu dasha.
Chaturtamsha Chart (D4)