And here's the story: Tigger must have caught the rabbit somewhere near our house, there are plenty of them around.
He even managed to bring it back home with him, through the catflap! We decided he could keep it, but he'd have to do the disassembly elsewhere, as it would very likely get messy. So Stoneshop moved both Tigger and the rabbit outside, only to find Tigger quite a while later, looking at the rabbit with a puzzled look on his face, as if saying: That looks delicious, but where is the opening tab?