In Elie Weisel's Night, why are the prisoners asked to stay behind in the camp?
Your question did not specify which camp you meant out of the three concentration camps that Eliezer and his father were moved from (Auschwitz/Birkenau, Buna, Gleiwitz); however, in section five of the book there is one prominent instance in which prisoners are left behind in Buna.
When Buna is being evacuated, prisoners who are patients within the camp infirmary are left behind most likely because bringing them along would slow the evacuation process down; many are too weak or injured to be able to run to Gleiwitz along with the rest of the inmates. Eliezer chooses not to stay behind with them in spite of his own injured foot because he assumes they will be killed. But he later learns that those left-behind inmates were actually freed two days later by the liberating Russian army when it arrived.