No, it's not fine - as the new owner of the previously honest business might be a total conman who's about to start ripping everybody off.
The only way to render the sale of an eBay business (inc ID) acceptable is to have the new owner state in LARGE print in every auction that he is not the person who earned the feedback points.
Failure to do so would render every contract invalid and every PayPal buyer could complain to PayPal and have their purchase money refunded from your account.
It would then be up to you to try getting your goods back.