First world countries' with shrinking populations aren't falling apart. Sure places like Japan, Italy, and Spain have economic troubles associated with a growing retirement population, and shrinking workforce. But they're still pretty good places to live in.
While global growth would decline, I'm dubious of the claim that per-capita wealth would go down. With the same pool of resources spread across fewer people, the opposite seems likely. The labor force would reduce in size, too, so manufactured goods and services may not see their prices go down. But things that are zero-sum like natural resources, real-estate, etc. should drop in cost as fewer people are competing for them.
From an individuals point of view lower population means fix resources are spread less thinly. There is less competition for jobs so you can command a large share of the pie.