Yes, individual countries like Japan have birth rates well below the replacement rate, and that will cause those countries demographic problems that will require immigration to fix (and Japan places a high value on the homogeneity of their society, so it would be a big change for them). China is another country facing a demographic hole, thanks to the 'one-child' policy that was continued much too long. In order to shrink the world's population without causing this sort of issue, a world
birthrate around 1.8 - 1.9 seems to be about right, below the replacement rate of 2.1 (for developed countries; higher for those with higher infant mortality rates), but above the level where you're facing what in China (2016 birth rate 1.62) is called the 4-2-1 problem: one grandchild will be supporting the retirement of two parents and up to four grandparents. The alternative is that better health care and lifestyles allow more people who want to work to do so as long as they want, or (as is being developed in Japan), robot companions will take over much of elderly health care and assistance.