In Night, what is Eliezer's plan if he is selected for death at Birkenau?
I think it is important to remember that this is the first of many selections that Elie undergoes, and as such, he is hugely confused and disorientated by the process. He has just been told to lie about his age and also chooses to lie about his profession, though he is not sure why this is imperative. In addition, all he knows is that the prisoners are being sorted by Dr. Mengele, who appears to be separating the prisoners into two groups by pointing the baton to the right or the left - Elie is not aware of which side is the one he wants to be sent to. His plan, therefore, is to end up in the same group as his father:
The baton pointed to the left. I took half a step forward. I first wanted to see where they would send my father. Were he to have gone to the right, I would have run after him.
Not knowing the meaning of "left" and "right", therefore, Elie determines to stay with his father, whatever the cost. Fortunately, or perhaps unfortunately, they are both selected to live and thus embark on the gruelling struggle for existence that is charted in the rest of the novel.