Well, if herd immunity is achieved only by a part of population, then decline will continue only to a point where all cases in that part of population will end,

Well, if herd immunity is achieved only by a part of population, then decline will continue only to a point where all cases in that part of population will end, but stay with the rest of them. In practice because groups of population are not isolated from one another it just means that amount of cases will decline to a certain level (dictated by time which it takes for the natural immunity to wear out, and fraction of population that hasn't reached herd immunity). In practice it may mean that virus is gone as a "problem" (remaining case load, especially considered that most vulnerable people are vaccinated to a higher degree in all groups of population, will be manageable for the healthcare system). But cases will never go to zero, and some unlucky people even most vaccinated groups will still get sick. Now on the level of individual country, it's not a big deal. On the level of the world ("if all countries apart from Afghanistan and Russia vaccinate almost all people, reach herd immunity in all groups of population, and their case numbers will go to zero"), it is very different. If we still have say 3% of the world population with the virus actively circulating, they will give us a vaccine-resistant strain sooner rather than later, and we are back to square one.