Japan is in a unique position in the world.
Being an island, they are well-positioned to keep out all non-Japanese.
Which, essentially, is what they do now.
So long as they CONTINUE to do that, their population can go into decline and it won't really matter in the long term.
It may even HELP.
Fewer people mean that wages will go up, the cost of living and housing will go DOWN.
They're technologically advanced to cope with this.
Their cities will become less crowded.
The key to the future is that (again, so long as they keep out foreigners, particularly muslims) Japan can grow "smaller" and WILL STILL BE "Japan". Populated by ethnic Japanese.
That's what counts for any culture to "survive".
Unfortunately, this won't be The West's fate.
It won't be ours, either.