An obvious example, before Cyprus joined the EU they were able to control their borders and you were vetted before you were allowed to buy/settle here.
Before EU we had to submit a written letter from our UK bank manager to the effect that we were solvent and would not be a burden on the Cy economy. This was then submitted to the Council of Ministers for their judgement. No problems with that.
They (immigration)are not now allowed to prevent any EU member from entry/settlement, regardless of means to support themselves - or not, as the case may be. It becomes a big problem, but of course plenty of cheap labour........that is until the EU pushes its minimum wage directive this way.