The resident permit is valid as far as the free movement of the person in the Schengen Area is concerned. Any citizen who holds a long-term visa (such as the resident permits for real estate owners) that has been issued by a member state and is valid is able to travel to other member states for up to 3 months within a six-month period, while he is also granted a right for multiple entries. These are the rules of Schengen Area. Of course, the movement among Schengen countries is not checked at the borders. Regarding the access to the Greek labor market, in no case does the resident permit for property owners provide access to any type of employment. But employment, according to paragraph 6, article 20, of Law 4251/2014, does not include the exercise of economic activity in the capacity of a shareholder or a chief executive officer for an already existing company.
Are there any residency requirements for Greek Golden Visa holders?
If I obtain the visa through the program, can I live elsewhere in the EU? What about working? If I can’t work in Greece, can I work somewhere else in Europe on my Greek Golden Visa resident permit?
You can work neither in Greece nor in any other country in Europe with the Golden Visa. You can live permanently in Greece and travel in other EU countries as if you had a Schengen visa (i.e., stay 90 days per semester).
You can travel and stay until three months with no restrictions to all Schengen countries. But in order to stay permanently there, you should follow the internal procedure of the state you will choose. A Golden Visa doesn't give you the right to work, so I don't know if the Schengen country you will choose can give you any work permit according to any legal procedure. You should ask a local lawyer. Anyway, you have the right to establish your own company.