Actually in the case of beavers they were mostly deliberately hunted. Beavers get along fairly well in close contact with people, they're happy to live in the

Actually in the case of beavers they were mostly deliberately hunted. Beavers get along fairly well in close contact with people, they're happy to live in the peripheral wetlands around the places we like to settle. But their natural behavior is to dam those wetlands, which tends to inconveniently flood the areas we're trying to use. So over time we killed them all, deliberately[1]. So, as long as you're willing to modern hydrology management around their areas to prevent damage, beaver restoration programs like this actually work very well. Beaver chew in suburban parks in the US west is a routine thing to see now. [1] Also it turned out they made inconveniently fashionable hats, which didn't help.