Blocking feature not working

Hi Elle1939,

Welcome to Apple Support Communities. I understand there's a contact that has been blocked, but you're still receiving their text messages.

Relying on making sure that a contact is properly blocked, can help provide a peace of mind. I'll be happy to help.

If you're specifically receiving voicemail messages from this blocked contact, then this is expected behavior and can occur. Text messages and phone calls are blocked. That information is outlined in this helpful article: Block phone numbers, contacts, and emails on your iPhone, iPad, or iPod touch

Now if this is not the case and you're receiving text messages. I suggest to temporarily unblock the contact and restart your iPhone. From there, please block the contact again.Then see if that helps resolve the issue you're experiencing. Here are the steps:

1. Go to the conversation thread in the Messages app of the contact you'd like to block and tap on the contact's name.
2. Tap the "i" > Tap the name, phone number or email address and scroll down to tap on "Unblock this Caller."
3. Restart your iPhone
4. Then, go back and block the contact again.

Please keep us posted with the results.

Kind regards.