The Japanese are in dire straits in the future, but for them, immigration is less palatable than in much of the rest of the world. The alternatives are to simply fade away, have some sort of controlled immigration scheme, or...well, take a drive around the ghettoes of Paris sometime, and you'll see what the third alternative looks like.
The Japanese will probably continue to make advances in Robotics...that will solve the labor problems they'll have in the future!