Den Vogel isst die Katze
How do you know it's the cat eating the bird, and not the bird eating the cat? Other than guessing from the context I mean, as most birds usually don't eat cats...
In this case you are lucky. Der Vogel >>den Vogel is Akkusativ. As there must be a subject (in Nominativ) the only candidate is die Katze. In this way Germans can change the word order without losing the content. Normal would be: "Die Katze isst den Vogel." Just imagine a phrase like: "Das Schaf isst die Falke" Neuter and feminine have an identical Nominativ and Akkusativ. You would have to realize the whole content and then know that a sheep is not a carnivore.... By putting the object first you give it a lot more stress than normal.