Jewish people could constitute the majority of a shtetl's population
but places were not "entirely Jewish". A shtetl might be artificially
"subdivided" into the Jewish and Gentile sections, which were often named,
e.g.. Velykyy (Large) Shtetl and Maly (Little) Shtetl, Vysoki Shtetl
(High, probably on top of a hill) and Niski Shtetl (Lower, probably
at the foot of a hill). In larger towns, Jews used to reside in separate
suburbs (Kazimierz in Krakow, Nalewki in Warszawa), while in smaller
towns they occupied certain parts of the street.
But to the best to of my knowledge, Jews could not hold any administration position whatsoever within the Russian Empire Territories, nor could they own land. All land available for distribution was been distributed amongst the Russian noble class following the divisions of Poland, or it was already owned by Lithuanian or Polish nobleman, and any remainingv real estate was Crown's property.
The original query (this was originally a response to a post on Jewishgen) was most probably refers to a starosta as an elder of the Kahal (entire Jewish community) or the elder of the synagogue, a person responsible for maintaining birth, marriage and death registration within the community, and following up the re-registration of those events with the local government administrator.
2. A title equivalent to starosta, called "wojt" [vuyht] in Polish, was used in Russian Poland untill 1863 when tit was been replaced with starosta as russification of the territories took the place.
3. Starosta in medieval and pre-divisional Poland (end of 18th century) was a higher hierarchy military-administrative function within Poland-Lithuania Commonwealth of Nations administration.
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