Copying database is legal in USA and illegal in EU. What happens if database, located in USA is being coppied, but the database owner is a resident EU

As a general matter, a person in the United States who is lawfully in possession of information and who has permission to copy it from the owner will not be subject to prosecution in another country for acts lawfully committed in the United States. Your facts are a little thin, and by beefing them up you might change the result.