In short, Pavel dies from Lieutenant Kotler’s beatings after Pavel spills wine on Kotler during a dinner with the commander of the camp and the commander's family.
In chapter 13 of The Boy with the Striped Pajamas, by John Boyne, Pavel serves as a waiter and vegetable chopper in the house of Bruno’s father, the commander of the camp. Pavel was a doctor before he was imprisoned in the camp, which Bruno found out one day when he fell, and Pavel was the adult who took care of him. Pavel is very smart, but he is Jewish, so we know he is not respected, cared for, or liked by the Nazis. Bruno describes Pavel as very old, having grey hair, and stooping over. Pavel is an older man who is not in good health. Bruno describes him at the dinner as standing there almost looking like he is asleep, with no life to his eyes and a slow response time. He also discusses how Pavel is becoming smaller each week, has shaking hands, and is steadying himself against the wall. These descriptions allow the reader to see just how weak Pavel is.
Considering Pavel's weakened state and Lieutenant Kotler’s anger toward him after the spilling of the wine, it likely wouldn’t be difficult for Kotler to kill Pavel when he is beating him. The reader can assume that Pavel is beaten, because Bruno is very upset about the situation and the fact that his father hasn't stopped it. He cries, and his sister goes pale. Although Bruno doesn’t ever directly state that Pavel dies, he does say Pavel is replaced by another Jewish man, and as Shmuel said earlier when they were talking through the fence, the Nazis are not concerned with the Jews getting better, so Pavel wouldn’t get medical help for his injuries. Through these pieces of the text, it can be assumed that Pavel dies after being angrily beaten by Kotler.