Let’s say it is 1950 and a young polish woman sees a German man who personally participated in the medical torture and death of her parents and brothers at Auschwitz. Enraged she runs up to the man and kills him on the spot.
There’s a lot of times where the law and morality don’t really match up, but I don’t think this is one of them. Sounds like she committed manslaughter with some mitigating factors. I’d say she should be prosecuted as such.
She should be arrested, but the prosecution would likely drop the case due to no real chance of a conviction. Not having been tried, she could be tried in the future should it turn out that she had been less than honest or not correct.
The OP doesn’t say where the killing takes place in this hypothetical. Given that a Polish woman and a German man were involved in 1950, it is most likely that it took place in Poland or in East Germany, both of which had Communist governments installed by Stalin after the war. So any result is going to depend both on the formal law of those countries, and on the attitude of the ruling Communist Party.
I took the OP as, the young Polish woman was in Poland in 1950. (Which was under Soviet control) If so, the KGB would investigate/interrogate. If he was found to have been a camp guard, she would be given a Hero of the Soviet Union Medal. Otherwise off to the Gulag.