What is actually being implied is:
Fyedka and Chava are having a serious relationship that no one knows about.
"Fiddler On The Roof" is known to be a musical which is based on Tevye and his Daughters (or Tevye the Dairyman) and other tales. The story was written by Sholem Aleichem.
In the story, Tevye, a milkman from the village of Anatevka attempts to maintain his Jewish religious traditions due to the external influences that came into the family life.
Chava is one of Tevye's daughters who later got married to Fyedka while Fydeka is a Russian villager and the husband of Chava.
Thus, what the given statement in the question implies is that Fyedka and Chava are having a serious relationship that no one knows about.
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