Order cancellation is known in DEAR as Void or Undo. Orders can be undone or voided at any point in the order.
You can use the Sale/Voided and Sale/Undo events in DEAR webhooks to be notified when an order is cancelled, and update your system using the SaleID in the payload. See https://dearinventory.docs.apiary.io/#reference/webhooks/webhooks for more information.
To be able to use webhooks, you should add the Automation module to your DEAR subscription. See Adding Trials of the POS, B2B, API and Automation Modules to Paid Plans for more information. You can also get more details from DEAR Customer Support.