Most merchants do not need to change these settings.
Please only make changes if you know how this effects what customers can return.
Example Unfulfilled Order: a merchant wants customers to be able to return an order as a quasi cancellation for their order when the order itself has not shipped, yet. Note that we do not cancel the order, this has to be done manually.
Example Pending Payment: a merchant wants customers to be able to return an order when payment is settled in cash (e.g. courier) and there is a time delay in registering the transaction (manually) so the customer can already initiate a return.
Example Authorized Payment: a merchant wants customers to be able to return an order when payment has been authorized on the customer's end but not captured on the merchant's end. A payment usually goes instantly from authorized to paid in Shopify.
In your Rich Returns dashboard navigate to Return-Settings / General / find the section below. Enable the options that fit your business processes and hit save at the bottom of the page.