Delivery Failure/Delivery Notification: Delivery has failed issues

When people receive emails which appear to come from their own address but they haven't sent they naturally tend to be concerned: however it's most unlikely that anyone has hacked their account, they've just been targeted by one of two common spammers' techniques: both arise because it's all too easy to forge the 'from' address on messages to be something other than the real one.

There are two things that can happen. One is that the sender has forged the 'from' address to be the same as the 'to' address (so other people will see it coming from themselves, not you), presumably in the hope of confusing spam filters. It's harmless, if extremely annoying. Delete it (never ever answer spam or try to unsubscribe from it), and you don't need to be worried about it.

The other problem - which appears to be what is affecting you - is that a spammer is forging your address as the 'from' address on a whole batch of messages. The first thing you hear about this is when you start getting bounce messages because the spam has been sent to non-existent addresses and is being bounced to you. There's no point at all in responding to it. It's infuriating but normally stops after a bit as they move on to another forged address.

There isn't really anything you can do about it: closing the account isn't really worth the hassle unless you are totally swamped, because you will have to tell everyone your new address. Apple can't really do any more than they already are about spam.

You could set up a Rule to move messages which have the failure warning in the titles to the Trash or a special folder. Of course this will also catch anything you get bounced that you send yourself, and since the wording will vary it probably won't catch all of them anyway, but it may reduce the annoyance a bit.