Dear Shirin,
These are very interesting questions. The migrant communities, in my opinion, suffer a lot more adopting to a new and totally foreign environment, than to say, adopting to gradual changes within their own environment (basically the same as what You and Muzna are saying).
The challenges to immigrants are far more resplendent than just a challenge due to fossilization. Since economic consideration has been (and still is) the main reason for immigration, the issue becomes multi dimensional. In my observation, newly arrived immigrants are more worried about finding a job than to retain their customs and cultures. Once that hurdle is crossed, then the second one is erect, which, in more cases than less, how to integrate into the new place and still maintain some of our inheritance. This stage is perhaps the most difficult one. Families are torn apart by the contrasting views of the members within the families. Some become totally absorbed into their new environment, and some still remain in their old, and yet some (I would guess most) find a balance.
The challenges to immigrants, and NYC is perhaps as good a place as any to study, are multi-dimensional, are not just cultural.
The buzzword these days is “Cultural Survival”, which has generated a very hot debate in many disciplines, and not just sociology. E.g., there is an engineering branch of hydroelectrics that is advocating stopping the building of dams in poor countries for the fear of displacing indigenous people, and therefore destroying their culture. The Greens of Europe are involved in such causes as well.
Back to your question how much it has impacted on Desi community. From “living here” point of view, I can say that it has a pretty hefty influence on how desis relate to non-desis. When some Desis travel back to Pakistan, they always complain that people in Pakistan have changed so much (I sometime suffer from the same symptoms). This is very challenging to any group of immigrants, also challenging to the natives who absorb such groups. They fear as much as losing their own ways of doing things, as the arriving immigrants feel.
There is a big debate about Fossilization of Languages. Since this area is relatively new to me, as I took my anthropology in the mid 80’s, I have not been able to stay current with new developments in linguistics. But I do know that this area of study is becoming a discipline within its own rights, as physical and social anthropology evolved out of sociology in the 50’s. I will be interested to know what your thoughts are.