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Your staff/volunteers can do this by clicking the 'Can't attend anymore?' link in the roster information when viewing the event details. From there, a confirmation box appears to confirm their intention to withdraw from the event, as well as provide a reason or comment if available.
When submitted, the system will mark their name as 'Withdrawn' from the event, and any reason/comment given will be added to the roster notes for the person.
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Event specific - This facility can be turned on/off for each event by editing going to the 'edit event settings ' page, and changing the 'Allow people to withdraw themselves' setting within the 'Staffing' tab of the 'Options' section. Changing things will override whatever has been setup in the group settings.
Default settings - The default settings can be found in the group 'configuration' page, where you can change the setting as required within the 'Events' tab.