Although it is rare, thank goodness, every once in a while a difficult buyer comes along, someone who doesn't pay, doesn't respond to emails and  then gets upset after you've followed proper Ebay procedure to get your Final Value Fees back and move on.
       They may still get angry when their item doesn't arrive, even though payment was never received. They may immediately start sending angry, abusive emails or even go so far as to call you about "their" item, even though weeks have gone by and no payment has showed up.
       Although you may feel baffled or mistreated by such hostile behavior and sorely tempted to respond in kind, don't give in to that urge. Instead, act like the professional seller you are and follow these tips to resolve the problem:

1. First rule: Always be polite, tactful and direct in emails. DO NOT use abusive language, no matter how much you feel you are being provoked.  Stick to the facts. Example: "The auction ended on August 2nd. In spite of 2 payment reminders, I have no record of payment received. If your check or payment was cashed, please provide information so we can resolve this quickly. I look forward to hearing from you so we can clear this up as soon as possible..." etc.

2. Of course, your life will be much simpler if you keep organized records of all payments received, dates any checks cleared your bank, shipping dates and delivery confirmations (I strongly recommend using delivery confirmations; they aren't foolproof but they sure lessen problems).

3. Keep records of everything and if you have not received a payment, be able to provide proof that you did not receive payment, either by Paypal or by some other payment method. If the buyer insists a check cleared, ask for detailed information about the check number, copy of a record, etc. Bank mistakes CAN happen and letters CAN let lost or misdirected. Assume the buyer is telling the truth unless you have reason to believe otherwise. Don't be accusatory or attacking. Try to stay neutral and open-minded.

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4. If the angry emails continue or escalate in intensity, keep copies of them, including headers. Forward them to Ebay's Trust and Safety Department. Speak with Live Chat if you have to. Ask for a supervisor. DO NOT sit by while someone threatens you physically, even in an email. Always err on the side of caution.

5. If the buyer has a history of nonpayment and bad feedback, point that out when you communicate with Ebay. If they are about to be kicked off, keep a close eye on the situation. As soon as a buyer is NARU (not a registered user) you have no obligation to continue communication or complete a transation. . On the other hand, if the buyer has impeccable feedback, you might consider giving them the benefit of the doubt and try your best to work out a compromise or start an investigation of the lost payment through the postal system. Remember, MOST Ebayers are honest and trustworthy (I say this as an 8 year veteran here).

6. IF YOU FEEL FOR EVEN ONE SECOND that you are truly in danger, forward any abusive or threatening letters to Ebay. If you receive a threatening phone call, notify your police department. Again, always play it safe.

7..Although you may find it hard to respond calmly and tactfully when someone sends an attacking letter, continue to try to  sympathize with the bidder. Perhaps they DID send payment and it never got to you. Perhaps they feel treated badly, even though you did nothing wrong. Perhaps they are having difficulties that have nothing to do with you and they honestly believe they sent payment and should have their item.

8. Try not to take it personally. The reaction may have little or nothing to do with you.  If you have an excellent track record and solid feedback, try to remember that one bad incident is just that - an anomaly, not a pattern. Relax. Breathe. Stay calm.