Maybe in another twenty years assimilation will have triumphed. That's really the only option, after all. European democracies will never deport millions of people no matter how bad things get, and at the same time the non-assimilating crazy-types will never be able to really turn Sweden into Syria or Sudan. They'll have to live together, and both dilute their cultures into a new, mushy one.
Or maybe something darker will happen. After all, this new European-wide era of liberal triumph is just a few decades old. World War II seems like a long time ago since the last veterans are steadily dying, but it only ended 68 years ago. Eastern Europe only shook off communism a little over 20 years ago. We take the stability and freedom of the West for granted, but there's nothing to say that it lasts forever, especially when put under tremendous pressure like is steadily building with this non-integrated immigrant problem.
But it's unbelievable things have gotten to this point to begin with. Europeans have too big of hearts and too low of birthrates to keep waves of immigrants out, and now, quite unintentionally I presume, the nation-state itself is rotting away. Again, that's not an inherently bad thing. The United States thrives on its not being a nation-state and basing citizenship on birthright and loose civic loyalty rather than ethnicity. But the transition from the homeland of a specific people to a homeland for all will be a rough one for much of Europe, if it can happen at all. Hopefully it does, but good God did they get themselves in a mess.