Their subscription is associated with the LiveID used to set it up. Changing the email address didn't change the LiveID - and the LiveID does not need to be the current email address.
however, since your customer has forgotten the password for the old LiveID, which is still the OneCare subscription ID, you have two choices (well, he does):
1. Contact support for help with getting the LiveID reset -
How to reach support (FAQ) - http://social.microsoft.com/Forums/en-US/onecareinstallandactivate/thread/30400b52-7f26-4ba0-bc18-17e305329d90 (Note that this probably means starting with email support)
2. (And I'd suggest this as being easier) - remove OneCare from the PC shortly before it expires, then reinstall it from http://onecare.live.com (download the trial) and then subscribe with a *new* LiveID - http://account.live.com - and purchase online (full retail price) during activation or use a retail key from a store bought copy ($29 at WalMart according to other posts today).
-steve
Microsoft MVP Windows Live / Windows Live OneCare & Live Mesh Forum Moderator