When you create an event in Duplie, you can also cancel the event.  To cancel an event, you need to be an admin or owner of the event.  When editing the event, there is an actions button with the option to Cancel Event...  Depending on if the event is a one-time or recurring, you will see different options.

Cancel one-time event - When canceling a one-time event, the default behavior is to send out notifications to everyone signed up, and then delete the event.  You can change this behavior with the config 'Event Cancel Delete Event'.  With this configuration, you can change the cancel behavior to mark the event as 'Inactive' instead of deleting it.  This will still send out the cancel notifications, but keep the event as 'Inactive' status so you can still view/clone the event in the future.  You can view inactive events by doing an advanced search on events, and unchecking 'Active Events Only'.

Cancel recurring event - When canceling a recurring event, you will be presented with various options regarding which date(s) to cancel.  The default is to cancel a single date (the date you were viewing).  Canceling this date will send out notifications and delete that date, but the entire event will remain.  The date you cancel will be permanently removed and cannot be recovered.