In the aftermath of the 1974 invasion by Turkey (wikipedia), Turkey induced 150,000 settlers to move to Cyprus in an attempt to tilt the demographics of the island in favor of Islam and Turkish control. The illegal settlers pushed the population of Cyprus over 1 million. The illegal settlers continue to be a focal point of contention today.
This game of countries using emigration to extend poltical control has existed since antiquity. Machiavelli wrote reams about colonialization.
When discussing large patterns of illegal immigration, one has to consider the reasons for the immigration.
Human history is full of rogues pushing people from one place to another to gain political advantage.
Unfortunately, an open borders policy doesn't work on a planet where the political leaders have taken to using migrations as a form of extending power.