You can allow your clients to cancel or refund their own order with a setting in Customization -> Options -> Auto Refund. 

When this option is activated, the customer will have a link in his Order page to cancel or refund his order. The current refund rules are being used so that refunds may be partial or even non-refundable. However, if the event is canceled or postponed, the refund will always be without penalty. The customer will be informed of the amount refunded and of the amount of the penalty before confirming the request.

Here are the rules controlling the auto refund:

  1. There can be no refund if the tickets of the order have been scanned.
  2. If the event has not been canceled, a refund can be done until the date of the beginning if the event as displayed in the calendar. To change this limit, simply change the refund rule that refunds nothing (100% penalty) for a certain amount of time before the event. You can always manually refund the customer at all times if necessary.
  3. If the is canceled, then the ticket can be refunded up to 60 days past the event as long as the electronic ticket has not been scanned (point 1).
  4. If the order is already canceled or has not been paid online (order made by the merchant) then the customer cannot refund himself.