Offenbach did that already.
Where you have the brigands' song about hiding and stealing be regularly interrupted by the Carabinieri arriving singing this:
We are the Carabinieri
We protect your family
But by an unfortunate twist of fate
In our defense of citizens ordinary
We arrive, we arrive, we arrive, always too late
Always too late
Always too late
Always
Too
Late
They completely fail to see the brigands "hiding" right next to them, and leave, and the brigands resume singing about stealing stuff.