Kyvelli, I am not a doctor to this matter, you can find many people here in, with much more knowledge to help you in this, (but I am not sure they would aprove somebody who tries to get easy informations without much study, which I partially respect as well from their side), yet here is a try (since I believe that when you have little knowledge and little time as well to study seriously, the only way to know more is to share your little with other people’s one):
The only rembetis I know, who died around 1945 (and this way comples with your criteria, since he is dead +50 year ago) is Anestis Dellias, one of the four members of the Famous Rembetiko Quartet of Piraeus (Rembetiki Tetras Xakousti tou Pirea) along with Marcos Vamvakaris, George Batis and Stratos Pagioumtzis.
He died from drugs and a song written from him as a profecy for his end is Είμαι πρεζάκιας or Ο πόνος του πρεζάκια and I am not if this is the same song or not. I wrote these in greek just in case you need to get them from the internet by searching.
Finally, I writte this in english because I am not sure you would understand full in greek and (as I get it) you need the informations for your effort.