If there is an valid extradition treaty with Ukraine then mr. Biden can be sent to them for trial if he is not president of the United States. At this time he is out of office and a plain citizen. If Ukrainian police have a good case and can convince a US federal judge then he can be sent there.
I read somewhere in a European article that there are other investigations (more than just Ukraine) regarding money-laundering in process. It seems some one on this side of the ocean would have publicized it.