Bear in mind there are 500 million eligible persons within the EU that may move to Finland if they choose. Once there they cannot legally be treated any differently to a Finnish native.
For instance as a French citizen if I find a job in Finland and want to move there, all I have to do is fill a EU form, and there I go. Finnish immigration is not allowed to throw me out of Finland, or deny me the right to work there, because it is my right as a European citizen to work wherever I want in the EU.
But, if I were to simply want to go live in Finland (without a job), I do think Finland is allowed to treat me as a perpetual tourist, that is to say not as a Finnish resident: no state benefits, etc. It might even be allowed to send me back to France, but I am not quite sure about it...