As Elie and his father are catching a bit of rest in a shed on the march/run to Gleiwitz, Rabbi Eliahu, his mustache ice-laden, finds the father-son pair and inquires about his own son. Elie notes that this rabbi's words always bring peace, and his countenance has never lost its innocence.

For three years, the rabbi and his son have endured everything together: physical abuse, starvation, and camp rotations. And now, the rabbi is in desperate search of his son, having lost him somewhere along the road. He notes:

We lost sight of one another during the journey. I fell behind a little, at the rear of the column. I didn't have the strength to run anymore. And my son didn't notice. That's all I know. Where has he disappeared? Where can I find him?

At first, Elie can't recall seeing his son, and Rabbi Eliahu leaves without any idea regarding his son's location. And then, suddenly, Elie does recall an important memory. As they ran, Rabbi Eliahu's son had run alongside Elie for a while. But the horrible realization Elie has is that the rabbi's son left him on purpose:

His son had seen him losing ground, sliding back to the rear of the column. He had seen him. And he had continued to run in front, letting the distance between them become greater.

A terrible thought crossed my mind: What if he had wanted to be rid of his father?

Elie realizes that the rabbi's son is no longer willing to risk death for a father who may not make it through this new form of torture. He prioritizes his own life over providing support for his father, and he does so without telling his father about his plan. He abandons his father in an effort to give himself a better chance of survival.

That night, Elie prays to God that he will never become the son that Rabbi Eliahu's son has become.

Rabbi Eliahu’s son ran away from his father to save himself. During the evacuation from Buna, the prisoners are made to run to the next camp at Gleiwitz. The German soldiers are unsettled and have orders to shoot and kill any slow prisoner. Thus, most of the prisoners at the back of the pack face the risk of being shot. Family members kept close, but in the case of Rabbi Eliahu, his son went ahead of him deliberately after his father stumbled. The son thought his father was slowing him down and putting him at risk. Fortunately, Rabbi Eliahou survives and looks for his son after he arrives at camp.

A terrible thought crossed my mind: What if he had wanted to be rid of his father? He had felt his father growing weaker and, believing that the end was near, had thought by this separation to free himself of a burden that could diminish his own chance for
survival.

Eliezer witnesses the events of Rabbi Eliahu unfold, and although he knows he is capable of the same act of self-preservation, he prays that it should not come at the cost of losing his father. Eliezer prays for strength to overcome the temptation of following in Rabbi Eliahu’s son's footsteps. Eliezer learns that it is possible for one to pursue self-preservation at the cost of family.

Oh God, Master of the Universe, give me the strength never to do what Rabbi Eliahu's son has done.

Elie remembers seeing Rabbi Eliahou's son during the run through the snow from Buna to Gleiwitz. Elie remembered seeing his son run up ahead and continue running without looking back.

He knows that the son deliberately ran ahead of his father to avoid being associated with him or near him at the rear of the line. Rabbi Eliahou's son chose "life" over family loyalty.  Elie sees Rabbi Eliahou's son as fickle and disloyal.

Elie promises himself that he will not behave toward his father like Rabbi Eliahou's son even if he is tempted. He does think of the extra rations he might be getting if he took from his father, but he puts this out of his mind and prays to God to give him strength and courage.

Elie proves himself to be true and loyal to the very end of his father's life.

Elie witnesses the rabbi looking for his son during the prisoners' life-threatening run/march to Gleiwitz.  The rabbi is convinced that his son would never leave him and continues his search.  Elie knows that Rabbi Eliahou's son saw his father stumble and become unable to keep up with the others, and he distances himself from his father.  The rabbi's son chooses self-preservation over family commitment (a major theme of Night).  Elie knows that he is capable of committing a similar act, and so for the first time in a very long time, he prays to God, asking Him to spare him from making the same horrendous decision about his own father.

In chapter 6, the Jewish prisoners are forced to evacuate Buna as the Russians quickly gain ground. Elie and the other inmates march in the middle of a snowy night as Nazi SS officers threaten to shoot anybody who stops moving. Elie compares the Jewish prisoners to automatons as they continuously march in the snow. Elie watches as several prisoners can no longer keep up the pace and are trampled by the moving pack of inmates.

When the Jewish prisoners finally arrive at Gleiwitz, Rabbi Eliahu asks Elie if he has seen his son. Rabbi Eliahu proceeds to tell Elie that during the journey, he could not keep pace with the other inmates and fell to the rear of the column. The rabbi tells Elie that his son didn't notice him losing ground and continued to march at a fast pace. After Elie tells Rabbi Eliahu that he has not seen his son, Elie remembers that Rabbi Eliahu's son had noticed his father losing ground during the march and purposely left him behind. Elie then thinks to himself that Rabbi Eliahu's son may have wanted his father to die in order to increase his own chances of survival, which is a horrible realization. Elie is glad that he forgot to tell the rabbi that he had seen his son and prays to never think or act like Rabbi Eliahu's selfish son.

Toward the end of the novel, Rabbi Eliahu enters the shed where the narrator and his father are staying. The rabbi is a kind, respected man who radiates peace, and he's searching earnestly for his son, who was separated from him in a crowd. Eliezer mentally acknowledges that the rabbi's situation is devastating, since the two of them had managed to stick together for three years through the suffering and the herding from place to place. The rabbi was feeling weak and was falling behind his son in the crowd, and the son didn't notice. At least, that's what the rabbi reported.

Eliezer's horrible realization, which he didn't share with the poor rabbi, is that he did see the rabbi's son in the crowd--and the son did notice that his father was falling behind...and the son just let it happen.

Eliezer muses sadly:

"What if he had wanted to be rid of his father? He had felt his father growing weaker and, believing that the end was near, had thought by this separation to free himself of a burden that could diminish his own chance for survival."

How does Eliezer respond to all this?

First, he's grateful that such a horrible remembrance had easily slipped from his mind. He's glad that he's forgotten--and presumably, eager to forget again after having pondered the situation for a few moments.

Second, he's glad that the rabbi doesn't know the truth. He probably thinks it's better that the rabbi is protected from the sad knowledge that his son left him behind on purpose. Searching for his son will give the rabbi hope, Eliezer probably believes.

Finally, despite no longer believing in God, Eliezer prays anyway. He asks for the strength to never abandon his own father.

The horrible realization that Eliezer comes to is more of a statement of what is as opposed to what should not be.  In the factory, after evacuating Buna, Eliezer and his father take turns sleeping through the night.  While awake, Eliezer sees Rabbi Eliahou in search of his son.  Eliezer realizes that the son abandoned the father while on the run in the belief that the father would not make it and survive.  The estrangement of father and son, and more pressingly, the abandonment of son from father fills Eliezer with a certain dread.  He hopes that he would not do what the Rabbi's son did.  He hopes that he will demonstrate the loyalty and commitment that the Rabbi's son so sorely lacked.  The horrible realization that Eliezer might be experiencing subconsciously, and that we know as readers, is that the true horror of the Holocaust lies in this condition.  While the Nazis and Hitler do represent evil, the very idea that any set of circumstances would demand that children abandon their parents in the name of mere survival represents the worst of the Holocaust.  This realization- the severance of emotional connection and bonds to one another and to one's own blood- is something that haunts at Eliezer, and serves as a foreshadowing for his own predicament when his father takes a drastically fatal turn in his health.