Block phone number completely
I have a contact that I have blocked and I continue to get voice messages from. How do I block the person from contacting me at all?
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Blocking a number on the iPhone will block the phone from notifying you, but it still allow them to leave a message without notifying you either. You can decide to either save the voicemail if there is a reason to believe there could be something of a threat or like that, or you can just delete the voicemail, that is up to you. However, there is nothing on the iPhone that can completely block the call. You can contact your cellular carrier and see if they can block that number or how to deal with it.