If you introduce small quantities of immigrants into a society, gradually, and they adopt local customs, if after 100 years the native population has been replaced after integration, does it mean that the original country and its culture have disappeared?
But a failure to assimilate, should the migrant culture become large enough, can result in the exact opposite outcome. Minority views seen as unacceptable may, over time, start to reach the point of becoming politically influential. So for instance, how likely do you think it is that a western liberal nation will criminalize homosexuality over the next 100 years? The question's ostensibly stupid. It's so far outside our trajectory and realm of thought that it seems about as likely as pigs learning to fly.
But just consider one example. Sweden today is one of the most liberal nations in the world with an extremely generous welfare state and an incredibly inviting people. They're also a very small nation of about 10 million people, not long ago it was less than 9 million. And their fertility levels have plummeted. At one point they were literally negative. And their embracing nature has also seen a near open door policy to migration, which is a big part of the reason that their population (and fertility) rates have increased. However, many of the individuals migrating are not assimilating - and hold views which are in extreme contrast to 'Swedish' views. If we assume Sweden continues along its current trajectory, it's not really out of the question to see what is today one of the most liberal nations in the world criminalizing homosexuality and beyond.
That is fundamentally what I meany by a people being exterminated. It's not the 'people' as in a genetic lineage, but the shared views and values that makeup a people. There will certainly be people that call themselves Swedes in the future. But the views and values of this nation may end up regressing (from our perspective) dramatically in the future. Centuries of progress and social development cast aside in what could be a matter of decades for a lack of fertility and a refusal to consider the implications of nonassimilating migration.
Can you point to any historical examples of the process you are describing?
As for examples though, we have to consider two major differences. First, extremely low fertility rates are extremely new -- even as recently as the 60s the US total fertility rate (average number of children per woman over their lifetime) had peaked at just a bit under 4. That already meant things like fertility did not really play a major role in these issues. And obviously as you go further back there is an upward trend.
The second issue is that widescale welfare systems did not exist mostly until the 20th century, and the great depression time in particular. You had things like poorhouses where people could exchange hard labor for a meal and bed, but these were extremely local and small scale systems. There would not be support for millions of foreign individuals unable to otherwise independently support themselves. As a consequence of this, mass migrations were effectively impossible. So you won't find today's scenario in the past, because it did not exist.
But I do think we can at least see rough analogs of this scenario play out practically everywhere that 'we' have colonized and decided to stay. Those were different times and war was often involved, but when you look at the times following peace things rarely got better for the natives. Once 'we' established ourselves disparities just grew over time and native views, values, and cultures were gradually relegated to an ever smaller piece of society to the point that, for instance, today in America we rarely even acknowledge Native Americans when speaking of things like 'minority representation.'
Well, that's because 90% of them had died, mostly from diseases spread by colonists, and many in war. Even perhaps genocide. So of course there's not much of their culture left.
But if descendants of immigrants from Central and South America become the majority, that's in some way a victory for Native Americans.
Also I expect that moving from a poorer/less-educated country to a richer/more-educated country will also effect people's values and beliefs.
One fallacy in this type of speculation is to assume that Muslims in the West will continue to have the same fertility rates they did in their ancestral countries. Maybe the first generation will, certainly not the second.
Give me your tired, your poor,
Your huddled masses yearning to breathe free,
The wretched refuse of your teeming shore.
Send these, the homeless, tempest-tossed, to me:
I lift my lamp beside the golden door.
I'm sure you'd agree they would not. The nations would rapidly regress/evolve, depending on your worldview, to what they originally were. So it should be clear that what makes up the "people of a nation" are the people themselves - and by that you have shared cultural, ideological, and other views. And with migration and cultural assimilation this culture can grow and expand, as has been the history of much of America. On the other hand cultures can also be completely replaced. For instance, imagine Islam continues to fail to really integrate into nations and, through raw fertility rates, starts to become the dominant factor in a generally liberal nation. What do you think would happen to LGBT rights? Women's rights? Freedom of religion and expression?
Nations, in the sense of geographic locations, will probably not be going extinct anytime in the foreseeable future. But the views and values of nations, particularly those that trend towards embracing social views, are very much at risk of going extinct in the future. And the most ironic part this is that this is all completely foreseeable.