I imagine the left would argue it will not collapse just continue to change. Do I personally foresee governments collapsing because of social unrest? This would require "migrant background" to reach at-least 30%. The prospect of a foreign nation such as Saudi Arabia/Iran etc militarily attacking an European nation is very slim.
So what is Western Civilization? To the left it centers on "European values". And when they criticize the far-right in Europe or May's recent comments about altering human rights laws in order to more easily seize, prosecute and deport individuals - they argue if we lose these European values while pursuing a solution/answer to Islamic radicalism then we have lost anyway.
When we look back at post-WW2 Europe; in terms of global influence we never recovered. Then even Asia over-jumped us. Economically/living standards relative to our competitors have also declined. This to me is more troubling. I image globalist would argue this cheap labor and influx of contrasting cultures/mindset will result in a more diverse thinking and *eventually* superior Europe. In the West's viewpoint, if multiculturalism is the definite way of the future then shouldn't Europe get a headstart and even take the leading rule?
USA is increasingly left (Democrats are going further into the wilderness in this regard) and today American culture shapes Western Civilization most. The USA is also the Wests military strength. An interesting combo to say the least. No matter how wild crime in cities such as Chicago turns, or how erratic you feel Donald Trump is - USA is the driving force and they are still quite stable. Without getting too far into NWO etc, I do believe fractured societies is a goal seeked by elitist. This ensures USA will most likely never experience a Russian revolution or even Solidarity movement.
IMO Western Civilization continues on but steadily worse off and more diluted. The influence (and control) will continue to increase alongside globalization.