You're right. Numbers of hopeful migrants gradually increase as the word spreads that they have a good chance in whatever country. I remember when Belgium was very open to Tibetan refugees that so many started leaving spontaneously from exile within India—many I personally knew. These were people that lived comfortably, not in camps or anything. Once the word got out that their passports (or whatever substitute) would get a "black mark" and they'd be unable to work and be denied government help, they just stopped going. This is just an anecdote, but it does make sense that if you have a good chance to start a new life in one of the world's best countries with government support, you'd bet your ass people would go for it.