Refugees coming to Germany is a well known fact.
But then, are there currently any German refugees leaving Germany and if yes, for what reasons?
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As @chirlu pointed out in the comments, there are other cases as well, for example a german family seeking asylum in the US who claimed persecution for wanting to homeschool their children. They were initially granted asylum, but later denied when the Obama administration challenged the decision, though they will not be deported.
Others are leaving Germany for religious/political reasons as well, but it's hard to say if they qualify as refugees.
There are reports about Jews leaving Germany because they no longer feel safe there.
(Edited:) I would still say that this is still a case of emigration, not a refugee situation. The UN defines refugees as people fleeing from a well-founded fear of persecution, so one does not have to wait for actual persecution to flee. But the Jews leaving Germany today are not fleeing to the nearest safe haven to escape a present danger, they decide to migrate to a place they like better.
There are, and always will be, individuals leaving Germany, or any other country. However, apart from individuals trying to escape their legal troubles, all other individuals leave Germany, in a legal and orderly manner.
The question boils down to what you define as refugee.
The other answers and comments list some instances of people leaving Germany. In some cases the individuals in question were avoiding legal trouble, as in the case of the “The Twelve Tribes” sect.
There was the instance of jews leaving Germany, yet there is little reporting in German media, and while individuals might indeed feel unsafe in their place of residence, I suspect a bit of political propaganda is in the mix as well, with Netanjahu proposing to jews in Europe to leave for Israel. If jewish people feel unsafe in their place of residence, moving to a different city would achieve the same ends, as leaving Germany alltogether.
In practice, a "German refugee" would be someone who moves from Germany to country X, claims that he or she is a refugee, and country X accepts that claim.
I know that if you come from certain countries to Germany, you won't be accepted as a refugee on principle. For example, if you come from France you won't be accepted as a refugee (French of course have the right to move to Germany anyway, but if they try to get accepted as refugees, that will be rejected).
The article about the "home schooling family" said that in 2008, four Germans (or more like four cases involving Germans, since the home schooling family had seven members) were granted political asylum in the USA. Which means, in 2008 there were at least 4 German refugees according to my definition (refugee = leaving + claiming refugee status + being accepted as refugee).
Now most Germans think that having to send your children to school is normal, and many people elsewhere will agree - but then obviously some refugees have more urgent reasons to leave than others.