What choice do Elie and his father make near the end of Night?

Assuming that you mean when Elie's father is near death, Elie struggles with whether to follow another prisoner's advice to take and eat his father's food in addition to his own.  The reasoning is that Elie's father is most certainly dying, and the extra food might sustain a healthier Elie.

However, this decision is extremely difficult because Elie's relationship with his father has changed drastically.  He goes from being embarrassed and rather ashamed of his father (because of his dad's inability to march or preserve himself) to trying to motivate his father through one more day and night.  As Elie has just reconciled himself to the fact that he desperately wants his dad to live, Chlomo's condition worsens.

Elie decides to take care of his father as best as possible.  He is a caring "nurse" to his dad in his last hours and puts himself second when it comes to his own needs.  Unfortunately, Chlomo passes away, and Elie is so emotionally and physically drained that he cannot cry at his father's death.  He almost feels "a sense of relief."