Backupify will not automatically rename a domain based on a domain name change on the Google Apps end.
The previous domain's users will become Archived, and if you wish to back up new data under the 'new' domain name, you'll need to set up a new account (or a new subdomain on the existing account), using the new domain name (using a Google App super admin account under that domain).
All of your 'new' accounts' would not include any data from the Archived users' account (but, that data still remains under the original accounts). We would recommend keeping any archived data under the old profiles, and utilizing the new profiles to house any new backed up data.
Unfortunately, there's no way to re-activate the Archived users under the old domain name, or merge the Archived and Active user accounts across the two domains.
Also, if a Google Apps username is changed (such as when a domain name change occurs), the system treats the change as if the previous user (with the old domain name/username) was deleted from Google Apps.
If you 'old' Google Apps domain name is completely shut down/inaccessible, please click here to submit a Support Request, or give us a call at 1-800-518-7449; the Support team will need to manually re-activate your user account so that you can access the backups.