Yeah the Tassie Tiger was sad. Farmers thought it was killing livestock but wasn't, just caught eating an already dead sheep here n there. Their love of open spaces contributed to their demise also so they say. Easy to hunt apparently. We are lucky our Wedgetail Eagle didn't go down the same path. It nearly did from over zealous farmers thinking that seeing one here n there feeding on a dead lamb carcass, that in reality died from frost, was killing the lambs.
They did end up controlling the rabbits using mixo, not a pretty sight seeing them with it, blinded by swollen puffed up pussy eyes slowly dying. It did smash them but they slowly developed tolerance to it and then calici virus was introduced along with baiting using poisoned carrots. Calici and baiting is still used. They still have managed to survive though, though not in anything remotely plague like.