In general, a declining population translates into a dying place. For a place (city or nation-state), dying can also refer to the aging of the overall population. If everyone is too old to work, then who will pay for the health care? Save the wildcard of migration, more deaths than births is an existential threat. "Low birth rates can actually pay off in the U.S. and other countries":
“Higher fertility imposes large costs on families because it is they, rather than governments, that bear most of the costs of raising children. Also, a growing labor force has to be provided with costly capital such as factories, office buildings, transportation and housing,” said UC Berkeley demographer Ronald Lee, an author of the far-reaching study to be published Oct. 10 in the journal, Science.
“Instead of trying to get people to have more children, governments should adjust their policies to accommodate inevitable population aging,” added Lee, who co-authored the report, “Is low fertility really a problem? Population aging, dependency, and consumption,” with Andrew Mason, an economist and senior fellow at the East-West Center. ...
... “A more complete accounting of the costs of children shows only a few countries in East Asia and Europe where the governments should encourage people to have more children,” said Mason, an economics professor at the University of Hawaii-Manoa. “In the United States and many other high- and middle-income countries, people are having about the number of kids that are best for overall standards of living.”
Low fertility is defined as the birth rate below replacement. The population shrinks naturally, which many people think is a problem to be solved. Intuitively, the fear makes sense. Social science exists to test the veracity of intuition.
In the best of both worlds, a community has low fertility and net positive migration. And in a perfect world, the migrants would hail from places with higher fertility where families bear the brunt of childcare costs. In this simple model, immigrants make up the replacement gap between birth and death rates.
To complicate this model, consider the younger dependents that will likely travel with the immigrant parents moving away from higher fertility costs. Without weighing the possibility that the immigrant parents will have more children, the second generation immigrants will likely have higher birth rates than the locals do when they start families. Often, the population bump associated with immigrants is more a function of births than the number of actual migrants. Temporarily, until the newcomer and tenured residential demographics converge (they always do), higher fertility costs return.
Don't take population numbers at face value. Ask about dependency ratios (young and old outside of typical working years supported by the labor force). During the peak of population in a given place, the high dependency ratio mostly consists of children. For the nadir of population in a given place, the high dependency ratio mostly consists of the elderly. Children of the population bust don't have pensions or investments. They haven't paid anything into the system. However, the cost for the care of the elderly in the population bust will tower over that of children. On the balance, it's much better for a place to be burdened with a high dependency ratio of elderly than a high dependency of children.