Feeling braver, I tried a more elaborate experiment.
On my iMac using the native Apple mail App, I created a new folder and copied a junk message to it. On my iPad, I could see the new folder and message, as we'd expect.
Back to the iMac, I deleted the new folder. On the iPad, the folder was still there momentarily but vanished as soon as I closed and reopened the mail App, forcing a refresh. I'm guessing you already tried that, or other means of forcing a refresh?
I'm now harbouring a suspicion that it may be your mail host, A&A, that is keeping some reference to your zombie folders. My own mail, that seems to work sensibly, is hosted by Google Apps or whatever it is called nowadays. Basically identical to gmail.
I'd suggest maybe try deleting and recreating the account, as originally suggested by g3uiss. If the new account recreates the zombie folders, seems to me that it would prove the A&A server has told the iPad they exist?