This is one of the sources that indicated Morris was from Tordobis. I asked the author of the book he wrote on the Arsenic Gang for his source and he would not provide his source.

Paul Mayerowitz

I found nothing when I googled Tordobis Ukraine or Tordobis Russia. 
But I did find something that might be a good resource for other places there: 
https://en.wikipedia.org/wiki/List_of_cities_in_Ukraine

https://en.wikipedia.org/wiki/List_of_renamed_cities_in_Ukraine


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Maryellen Tobiasiewicz
m_tobiasiewicz@...
family from: Bielsko-Biala powiat Poland
Gorlice powiat Poland
Lviv Oblast Ukraine

I am not sure if this helps, but there is reference to Tordobis, Russia online at https://murderpedia.org/male.B/b/bolbermorris1.htm
As it appears Russia and Ukraine keep changing ownership of realestate, this might be a reference to the town you are looking for.
Best of luck to you.
Rollie Stamps

I have determined that my family roots were in Krisover, modern day Krivoye Ozero. I reached this conclusion after reviewing numerous immigration papers and a document listing the Jews of Krivoye Ozero from 1920-1921. A cousin, who was brought to this country by my grandfather, was in a book about Philadelphia. The author stated he was from Tordobis. I contacted the author, who would not cite his source. Another individual’s website also cited Tordobis as his birthplace but could not provide a reference source.  --