To find Icek's family, I searched the database under the exact spelling for the last name Oblasty. It returned three other individual's names that shared the same address as Icek. Golda (1899) is the oldest female listed at the address, and I believe she was his mother. Gitla (22.11.1922) and Szlama (01.09.1925) are the other two children listed at the address, and I believe that they were his siblings.
I then searched under the fuzzy setting for the last name Oblasty, and received 3 matches for having the same address as Icek with the alternate spelling of Oblasly. Jakob (28.12.1893) is the oldest male listed at the address, and I believe that he was Icek's father. Golde is just a variation of the name Golda that was listed under Oblasty as well (I believe), and she was Icek's mother. And Szloime was just a different spelling of Szlama (as was listed under Oblasty), and he was Icek's brother I believe.
Golda, Icek, Szlama, and Gitla all have a tranport date of September 10,1942 listed in their notes (under Oblasty). This date falls during a week in September where the elderly, infirm, and many children were transported to Chelmno. I believe that the Oblasty children and their mother perished at Chelmno int he gas vans, based on this specific deportation date.