Not so sure, except for a last few holdouts in Spain about 40k years ago, who were probably whipped out by natural catastrophe along with regular humans in that area.
I think we kept diluting their gene pool by having sex with them and out breeding them.
For most people, except sub Saharan Africans, we are also talking about our ancestors when talking about neanderthals. Most of those bones we see on museums are probably the great x grandfathers of many people walking past.
Obviously we have no idea what happened over huge parts of deep human pasts, Neanderthals were a sparse population to begin with, and absorbing their people into the rest of humanity just by fucking is certainly a solution