The Soviet Union did not rescue Yakov, and there were rumors that Stalin and his eldest son had a bad relationship. They seldom meet each other, and only have family dinners on Stalin's birthday in a year. However, Stalin should not refuse to save his son because of his bad relationship. The reason why Stalin didn't want to save Yakov was probably one of the regulations that Stalin personally revised, ordering Soviet soldiers to die rather than surrender. If they are caught, it will be treason.
Stalin not only refused to exchange his son, but also arrested Yakov's wife and other family members in the early days of his capture. After his arrest, Yakov was desperate. Yakov finally chose death. He ran to the barbed wire, chose the high-voltage power grid and committed suicide during the discharge time in the concentration camp. In order to save his son's life, Khrushchev didn't respect his face, so he went to beria and Stalin and knelt on the ground to plead.
Khrushchev likes his eldest son very much. Unlike Stalin, he loves his children very much. Khrushchev was desperate when he learned that his son was captured. He was very happy after being rescued, but he soon received the news that his son was going to be shot.