Assimilation (or lack of) works on both sides. Go to any Asian country, and if there are a group of foreign expats there, good chance that they will seek out western restaurants, go to western style bars, buy western style groceries, and in many cases, not learn the local language.
But, this is somewhat of an unfair compare, becuase most of these people are not true immigrants, but retiring people and not really any chance that they (or their families) will be there for many generations.
Also but, in the defense of the expat, no matter how long they live in a foreign country (speaking mainly of Asia), they are never really "part" of the country. They will always be looked at as a foreigner.