eBay did not refund him, he opened a case and closed it,
Does he even have a case against me?
If it shows delivered, then technically no, especially since the case has been closed already. If you get it back, it's up to your own conscience whether you want to refund him or not.
However if you don't get it back, there is definitely no need to refund.
He also has the power to leave a negative, so bear that in mind too.