The subclient shouldn't be deleted that's why it's not available.
It contains "\" of the data in your backup set so it's possible to back up everything using it or by creating subclients like you did to specify the usefull data on your clients. The subclients are mutually exclusive so you excluded the content in yours from everything else and by scheduling the backups for it you get your valid backups. The default subclient content you simply don't schedule.
More info: http://documentation.commvault.com/commvault/v11/article?p=features/subclients/c_subclient_overview.htm
Hope this helps