Predators can eliminate the population of prey. But I am aware of the predator/prey cycles and how they are usually in a state of equilibrium. But that doesn't make it true 100% of the time.
Sorry, I should have said animal predators. Humans are different. And thinking about it even that isn’t accurate.
Introduced predators have indeed wiped out native species with no defenses many places around the world.
But I think what I said is almost always accurate for native predator/prey relationships.
There is a long-standing theory that humans wiped out most of the native mega-fauna of the Americans around 12000 years ago. I used to think this was ludicrous. Just too large an area and too many animals.
But read an article about a consistent trend. Humans reach Madagascar, Oz, New Zealand, etc. and within a century or two the megafauna disappear. Very consistent pattern. The Americas would just be the largest example.
Only exception is Africa/Eurasia, where the theory is that the megafauna co-evolved with modern humans and were therefore less vulnerable.