That's why they have questions they can ask you (online or over the phone) to reset your password. If you never set up questions, this might complicate things.
Also, MANY internet providers offer email-only service, for $10-15/moth. I've used this a couple times when changing ISPs. Kept my email going for a month or two after I switched, until everyone I knew was using the new address.
This was a BIG thing for AOL as people went to broadband, I know people that to this day still pay ($5/mo?) to keep their AOL email address.
I work for the Department of Redundancy Department