what happens if EU members overturn their democracies?

I’ve had several moving conversations recently with democratic reformers from southeastern Europe. They are near despair about their respective countries. Instead of quoting their confidential assessments, I’ll cite this summary by Tamas Dezso Czigler of LSE:

I have previously written a great deal about Hungary; the latest development is that the government has changed the election rules once more, and introduced the anti-democratic pre-registration of voters, which further heavily distorts the election system. The government also continues to fire judges, even though the act which made this available was annulled by the Constitutional Court. In Romania, the problems are similar and obvious – the government simply does not respect democratic institutions like the Constitutional Court or the President.

Both Hungary and Slovakia have seen the possibly racially motivated murders of Roma in recent years (including children). In addition, Slovakia has introduced a heavily anti-democratic language act, which bans Hungarians from speaking Hungarian in government offices, even if the client and the officer both belong to the Hungarian minority. … There are also fears as to whether Croatia will be able to stay stable, since it has had an even darker history compared to the others. And we hear news about extreme corruption in Bulgaria every day.

Czigler does not happen to mention the strongly anti-Semitic rhetoric in Hungary and Romania. That isn’t the primary issue; I think Jewish residents will be safe against outright violence, and they are few. He is right to highlight the murders of Roma. However, given the historical role of anti-Semitism in this region, it is distressing that explicitly anti-Semitic parties can capture large shares of the vote. This is a sign of deeply anti-democratic and illiberal tendencies.

I would be the first to recognize that US states have also passed “anti-democratic pre-registration” provisions and laws targeting language minorities. But the question is not whose democracy is better. The question is what to do about anti-democratic threats in Europe, given the fragility of the continental system and the importance (to the whole world) of making it work.

Thus I wonder:

A nation must be a democracy to get into the EU. Once it’s in, what happens if it backtracks so that it would no longer meet the specific political criteria for membership? And what happens if a member drops all pretense of democracy and goes the way of Belarus?

EU members face judicial review at the European level. But the governments in Romania and Hungary are contemptuous of their own nations’ courts. What happens if EU members simply ignore the European Court of Human Rights?

I am told that some Hungarian Jewish families have fled to Austria. If true, it implies that there are already refugees of one EU nation in another one. How would the EU handle larger flows of political refugees?

The anti-democratic parties are mostly far-right and nationalistic. That may make coordination somewhat difficult, because a Greek nationalist doesn’t intrinsically care about Hungarian nationalism, for instance. In the 1930s, the attempt to build a Fascist International “was marred by serious conflicts between the participants.” Yet the far right of the various EU member states have common enemies and can do a lot of mischief together. Will they unite?

At least in Romania and Bulgaria, an underlying cause appears to be corruption, meaning the political power of economic oligarchs. Can European economic policy constrain them?

Will the EU ultimately make its weakest members more democratic and liberal, or will those states make the EU as a whole more authoritarian and illiberal?

How do members with deep civic traditions but poor current systems of government (Italy, Belgium) fit into the picture?