Let's just be simple about this: pensions and oth3r old age support. Who pays for those? Young people. If young people have to support a lot of old people, you're gonna have a bad time. Everyone. The young people have have larger amounts taken out of their pay and old people who get less support because there are just literally not enough resources. And because old people outnumber young people young are pressured more and more under democracy to give more to older people.

That is only one terrible thing from demographic collapse.

Basically every government planned for what has been the norm over the entirety of human history. Which seemed logical up until recently. That means for decades policy and economic decisions were based on the idea that every generation would be equal to or greater in size than the previous one.

The knock on effects of these assumptions are the reason government pension programs like social security are a concern world wide. People are living longer and less people are paying into the systems. This is an issue with nearly all government programs. There are less people paying taxes, paying into social programs. Costs are not going down anytime soon. It's a recipe for instability.

Economic collapse, to a greater or lesser extant depending on how fast adjustments are made. Though in some cases adjustments cannot be made. Worst case societal collapse (think violent revolution).

Pretty much the entire world economy is based on growth. Individual countries economies for the most part are also based on growth. In either case part of the growth is in population so there are more consumers. Additional most societal institutions and jobs require having a certain number of people to function for everyone. Different countries have different critical jobs and institutions. Care for older population is a big one in most places, doctors, nurses, in home care, and people to do things for the old they can't do anymore. Too few young people means likely too few of those people to take care of older population. That in turn either means the state has to pay more to get more people in those jobs, or care falls upon family which can force them to work less (or quit completely). More money spent by government means less spent somewhere else, some of that will be critical or at least inconvenient for someone. Family working less, or quitting altogether, means they are no longer adding to the economy and become a drag. Further a ballooning older population can lead to a drastic drop in tax revenue and compound the drag on the economy they are already having. GDP can drop which can devalue a currency, then leading to increased costs for imports and borrowing. This can further discourage people who would otherwise have children to not have any. Once this gets into a positive feedback loop it can continue to get worse faster than a society can adjust.

Everything is interconnected in our economy inside any one country, but also across the entire world. A positive feedback loop (like the mortgage crisis the US) can lead to a recession, or worse a depression. Then people are out of work and might not be able to afford the means to continue living, they then can become desperate. This can lead to a crisis and even revolutions (has happened before).

Too big a drop in population guarantied to cause societal collapse? Of course not. It doesn't even guarantee economic collapse, might just be a recession where most people survive fine in the long term. It might all be fine. What the outcome is really depends on how well positive feed back loops caused by a drop in population are handled, and if they happen slow enough they can be handled. Lots of the Western world is in trouble, but a population drop might help climate change, it also might not if a positive feedback loop (permafrost methane) starts accelerating climate change.