old email won't still being used by hacker

I have an old comcast email address that was being used maliciously. I was receiving malicious emails and so I changed my comcast email by creating a new one. I thougth this woudl by default cancel my old one. However, a family member has now received an email from that old email account of mine with a link, obviously malicious. How do I make sure that email account cannot be used? Obviously a hacker is using it. Unclear to me. Thanks.