What would happen if all the ATP production in living things suddenly ceased?

Cell Death

What will happen is that organism dies within no time.

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Adenosine Triphosphate (ATP) is one of the products produced in glycolysis and cellular respiration. Thus, it is commonly associated with the term "energy". Since ATP is the energy source of cells, it is an essential element in the machinery of the entire system. Without energy, some of the processes in the cell like active transport, cellular respiration, electron transport chain, and other cellular processes which include ATP as pre-requisite, would not work.

Cell, in general, is a very busy system. If these processes cessate because there's no energy in driving the other elements to work, the cell would eventually die, as well as the organism (an organism is a packaged form of different organs consisting of tissues and tissues consisting of cells).