When adding a user, there is a setting in the Calendars Shared section to specify the default permission to apply for new sub-calendars that are added to the calendar.
The safest setting is to select Not shared. This ensures that users are not given access to new sub-calendars if they should not have it. You can modify user permissions as needed to grant permission to new sub-calendars, if appropriate.
If you are using a secure link to embed a calendar or share it with a group, the same recommendation applies. For best security, set the default permission to Not Shared to avoid accidentally including new sub-calendars in an embedded calendar view.

See also how to review and modify who can access each sub-calendar.