The plants would ultimately die. Although the plants won't need oxygen to make photosynthesis occur, it would be unable to perform cellular respiration. They will be unable to respire and produce the product of cellular respiration which is CO2 + H2O + Energy. These are necessary reactants for photosynthesis. Eventually, photosynthesis will consume more CO2 than it produces with cellular respiration. They won't have a sufficient food source and eventually die off.
If all the oxygen is removed from a terrarium, the plants would eventually die due to their inability to perform cellular respiration, which is necessary for generating energy. They may continue photosynthesis until their stored energy is depleted, but without respiration, they cannot sustain themselves in the long term. Oxygen is essential for the energy production needed for plant metabolism.
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