The end of 1 Henry IV is no ending at all. Hal and his father have been reconciled, and, at least for now, Hal has behaved in a princely manner. He has dispatched his rival, the rebel Hotspur. One Henry down, one to go. But just as this battle is not the whole war, and just as the last lines of the play see the king reorganizing his forces to continue the fight against the rebels, so too Falstaff is an unresolved and perhaps unresolvable figure. To adapt a phrase from a different context, perhaps he is simply too big to fail.
