The biggest problem facing the growing preponderance of elderly people in developed countries is the very low (for a couple of generations) fertility in developed countries. Japan doesn’t have elderly people committing crimes so they can be cared for in jail - as opposed to not at all - because Niger has a high birthrate.
No, Japan's problems aren't due to Nigeria's high birth rates, but many of Nigeria's problems - poverty and crime - are partly due to the fact that people in the slums are having many more children than they or their nation's economy/infrastructure can reasonably provide for. And many of the developed world's problems with mass immigration are due to high levels of immigration from more fertile Third World countries.