The study of the physics of a nuclear chain reaction as a sequence of fission cycles has established a positive effect of asymptotic limiting of nuclear reactor power after the insertion of positive reactivity and raised the question whether a similar power asymptotic after the insertion of negative reactivity would occur, which could lead to the failure of the emergency protection function of the reactor to establish its subcritical state. The purpose of this paper is to study the power behavior of a point nuclear reactor during staged insertion of large negative reactivity and the performance of the emergency protection of the reactor's nuclear safety requirements for stopping the fission chain reaction. The study is conducted by solving the kinetics equation composed in the representation of the nuclear chain reaction as a sequence of fission cycles. It is established that activation of reactor emergency protection does not stop the chain reaction due to the formation of a secondary chain reaction on delayed decay neutrons of accumulated precursors. It is shown that the reactor can be brought to a subcritical state if a slow core insertion system, such as fuel burnup compensation, is started in parallel with the emergency protection system.