Is that such a bad thing though? Foreigners can have rich cultures that don't necessarily have to be in dispute with your own. I know I learned quite a bit from the time I was living with a Russian flatmate for instance, but his influence doesn't make me "less German". I'll never understand why people are afraid of cultures different from their own when they could be embracing them. Chances are, you'll find something interesting if you just go into it with an open mind.
Indeed, foreign cultures can be rich in tradition and a country can certainly adopt foreign traditions.
At the core of a culture there are values/principles and a political ideology which is what drives the country and keeps it healthy.
When the core values/ideology/principles of a foreign culture influence your own country then that is when cultural decaying occurs.
It all depends on the receptiveness of the country receiving these foreign influences, there are countries who naturally resist to foreign ideologies/values/principles influencing their own.
America, being the melting-pot of immigrants it is, is much more susceptible to foreign ideologies.
I am not saying cultural decay is a bad thing, but radical changes in a culture's ideology can lead it to a chaos or even a civil war, as a new generation of citizens who have essentially grown in a completely different culture strive to take control of the country. After that comes a period of stabilization and then "normalization" as the country completely absorbs its new values.