Whether a registered customer is skipped depends on how you're targeting them:

• Automatic segments (E-commerce, Loyalty, Subscriptions, etc.) skip anyone who is suspended, has no email on file, or has Receive Email off.
• Lists (uploaded/grouped contacts) only check that the person has an email on file and Receive Email on — a suspended customer can still be added to a List and will still receive the campaign.

Receive Email is the customer's own opt-in: they can turn it off in their profile, or an admin can untick This user receive EMAIL? (shown as "Receive Email?") on the customer's account. On the List's contact page this shows as a Can Receive Email: Yes/No badge. Turn it back on (with the customer's consent) or fix the email address, then re-save the campaign so the audience is rebuilt.