When an Amazon customer requests a return but does not actually send the product back, as a seller, you need to follow the Amazon platform's policies and procedures to handle it.

Here are some basic steps:

1. **Confirm the reason for the return**: First understand why the buyer is requesting a return. If it is due to product problems or mismatches with the description, make sure your return policy is clear and communicate with the buyer.

2. **Contact the buyer**: Contact the buyer through the Amazon platform's communication system to ask if they have mailed the return product. Sometimes there may be a logistics delay or the buyer forgot to provide a tracking number.

3. **Provide guidance**: If the buyer did not mail the return product, you can provide them with detailed instructions on the return process, including information such as how to pack, the mailing address, and whether they need to pay for return postage.

4. **Set a deadline**: Give the buyer a reasonable deadline to mail the return product, and let them know that if the return is not received within the deadline, you will not be able to complete the refund process.

5. **Update return status**: If the buyer does not return the product within the time limit, you can update the return status on the Amazon platform to "Not Returned" or similar status so that the platform is aware of the situation.

6. **Submit evidence**: If the buyer insists that the product has been returned but has not actually been mailed, you may need to submit evidence to Amazon, such as logistics records, communication records with the buyer, etc., to prove that you have tried your best to resolve the problem.

7. **Request Amazon to intervene**: If the problem cannot be resolved, you can ask Amazon customer service to intervene and help mediate the dispute. Please make sure you have sufficient evidence to support your position.

8. **Consider refund**: In some cases, in order to maintain good customer relations and store reputation, you may consider refunding the buyer without receiving the return. This depends on your judgment and company policy.

9. **Learn from the experience**: Regardless of the outcome, you should learn from this experience and optimize your return process and customer service strategy to prevent similar problems in the future.

Please note that the specific policies and procedures of the Amazon platform may change over time, so it is recommended that you regularly check the latest Amazon seller help page or contact Amazon customer service directly for the latest information and guidance.