Why D7 Update Manager keeps sending emails? This is very weird,

http://example.com/admin/reports/updates/settings

keeps sending emails to my email while the owner of example.com has changed his website from Drupal 7 to weebly! I mean, the Drupal installation does not exist!
Update Manager is a module that exists and works inside your installation. This means that Drupal installation exists. Maybe it is no longer connected to domain, but it is there, up and running. Delete it and you'll be all right. Or, if you want to keep it for backup / rollback purposes, ask your sysadmin to delete it's CRON rule. Without system's cron and visitors, nothing will trigger update checks and mail sending.