Since the release of iOS 7.1.1, Apple presented a new security mechanism in all of the iOS devices that requires the owner of the device to disable Find My iPhone before an iCloud account could be deleted or the iOS device could be restored.
Well this, obviously, requires access to the password associated with that Apple ID of the device. The whole system was heralded as a great step forward for Apple Company. Unfortunately it appears that it is not completely secure, after the discovery of a flaw i iOS 7.1.1 that permits the whole process to be bypassed quite easily.
Further details and step-by-step guide to delete the iCloud account without password can be found below.
1. First go to the Settings > General > About and make sure you have the iOS 7.1.1.
2. then go to Settings > iCloud > Find my phone
3. Hold down the Find My iPhone to left and tap delete account whilst holding it. Some time it has some delays; but it should pop-up a dialog; with three options “Keep on my iPhone” “Delete from my iPhone” and “Cancel”. Tap “Delete from my iPhone” and then immediately tap the “Find My iPhone” again; when the pop-up opens up again asking for the password; tap Cancel.
4. Now go to iCloud settings and delete the iCloud name, simply erase it. (do not tap done)
5. Now hold on to your power button and turn off you device. (slide to power off) and then hold the power button again to turn it back on.
6. Turn back on your device. Now go to Settings -> iCloud.
7. Now tap on the Delete Account it will ask you to delete the iCloud account again twice, tap on Delete each time.
8. It should start deleting. As simple as that. To prevent this make sure you have a passcode on your device, something like this could be done to your device in matter of 5 minutes by anyone.
If you have any questions feel free to ask below.