Normally, Antigone would be stoned to death for defying Creon's express orders not to bury Polyneices's body. But Creon cannot do that; he has to make an exception in her case. The reason is that Antigone is related to Creon; she's his niece. Not only that, but she's engaged to his son Haemon. According to the ancient Greeks the killing of a relative would bring down divine vengeance, not just upon the perpetrator but the community as a whole. So instead of having Antigone stoned to death, Creon decides to have her walled up in a cave. Although this will lead to her being starved to death, Creon will still be able to evade responsibility for it. Clearly, he thinks there's a difference between actively killing someone and just letting them die.

Creon's approach to the problem is ironic indeed, not to say hypocritical. He's expressly forbidden Antigone from burying her brother even though doing so could well incur the wrath of the gods. Yet when it comes to sorting out a problem of his own making—the execution of Antigone—he's quick to hit on a solution that cynically invokes divine law.