Can you put into words the strategy the USSR had when taking half of Poland?

I would not say the USSR invaded Poland to save the Polish, although arguably many Poles were saved from Nazi extermination. Rather, they invaded Poland to save the USSR, hoping that keeping up their end of the bargain would actually prevent a direct war with Germany.

The Soviets knew the USSR would probably be invaded by Germany (Hitler literally says he wanted to invade the USSR in Mein Kampf and there are unarchived documents showing that this was indeed something discussed by Soviet leadership), but Stalin did not seem to be very confident that the USSR could win a war in its poor state. He tried to make a deal with Britain and France, offering a mutual defense treaty to keep Germany at bay, but was turned down.

Since the Soviets couldn't get any western countries to back them up, they decided to just make a deal with the devil themselves, and tried to negotiate a non-aggression pact (not an alliance) with the Nazis directly. The Nazis agreed, but with the condition that the Soviets invade Poland, since Nazi Germany wanted Poland and thought a two-front war would make them fall very quickly.

The Soviets also invaded only up to the Curzon line, which was not even historically Polish territory. The land the Soviets invaded had not been part of Poland for centuries, but imperialist Polish leadership wanted to restore the glory days of pre-1772 Poland so they invaded the east in 1919 to try and expand their territory.

Given how the communists in Russia promised to end the wars, and that the Soviets really needed those wars to end to be able to build up its economy, Lenin ceded territory to Poland in 1921 under the Treaty of Riga. It only was under Polish control from 1921-1939. It was not even rightfully Polish territory in the first place, and still to this day modern Poland's eastern border is on the Curzon line. Cities like Ivano-Frankivsk in Ukraine and Brest in Belarus are part of the land the Soviets entered, not modern Poland. These territories were never part of Poland except from 1921-1939 when it was bargained away to try and reach a peace deal with Poland.

/r/GenZhou Thread