I've read something, not quite sure where, hence my question. It said that once (I think about 50 thousand years ago) human population was as low as few thousand and was nearly extinct.
For me a few thousand is such a low number that I call bullshit. Can anyone confirm/ deny it? Point me to some works about such 'crisis'?
Or maybe was there a different time where human was close to extincion?
I think what you did come across was a reference to the Toba supereruption, an event 75.000 years ago which did have a huge climate impact.
There is a theory that this eruption was the cause of a shrinkage of the homo population at the time.
As this event predate "history", I am not sure it is in topic for this sub. I did a search for any past thread that mention it but right now reddit search is failing ...
Here is a past thread that talk about the effects on the human population of the Toba event.
No, not in history, but there have been suggestions that the human population encountered a "bottleneck" like you describe in prehistory. Richard Dawkins mentions this theory and points to the level of genetic diversity as evidence for it in- I want to say he talks about it in The Ancestor's Tale, among other places.
However, the bottleneck hypothesis has lost some support in the last decade as more evidence has accumulated.
On a related note, it really doesn't seem to take a huge population to 'seed' a large area. There's a study here that suggests that the founding human population of North America numbered about 70.