Will extinction occur within 20 years of the human population falling below 400 million, if the population falls that much by 2100?

Previous questions asked whether the human population would be reduced by 95% or more within 25 years of various catastrophes occurring before 2100, if such catastrophes occur. (The catastrophes in question were a global biological catastrophe, an artificial intelligence catastrophe, a nuclear catastrophe, a global climate disaster, and a global nanotechnology catastrophe.)

Such questions are especially important from a longtermist perspective and if they are diagnostic of the chance of extinction or some other existential catastrophe. Indeed, the questions were framed as partly intending to get at extinction risk. But how likely is extinction, given a 95% population loss?

(See also Will humans go extinct by 2100?, How long would humanity take to rebound from a global catastrophe?, and a soon-to-be-released question intended to get at the likelihood of unrecoverable collapse given a 95% population loss.)