You shouldn't need to create a new status set, just edit the settings of the status set in use, and in the column for "Automatically set when not marked" - select one of the status values to be used when the unmarked process is triggered.
You shouldn't need to create a new status set, just edit the settings of the status set in use, and in the column for "Automatically set when not marked" - select one of the status values to be used when the unmarked process is triggered.