When I got this message, I called Cox. they told me to go to webmail and delete everything there. but the new system is supposed to delete the webmail as soon as I delete the email from my desktop. so I wonder if the message you are receiving is spam? if you click the down arrow to the right of the sender's name, it will tell you who really sent it.
One website had a contest to see who had the most emails in their inbox. the winner had 17,000 undeleted emails in his inbox. 2nd place had 16,000. a few days later, they learned that one person had 42,000. all 3 users said that they used the Search feature to find the emails they wanted and never had any trouble navigating their inbox.