Can someone explain to me how 2,3 BPG works for hemoglobin?

BPG affects oxygen binding affinity by binding in a small cavity at the center axis of deoxygenated hemoglobin. In oxygenated hemoglobin, this cavity is too small to effectively accommodate 2,3-BPG. When bound, 2,3-BPG stabilizes the deoxygenated conformation of hemoglobin, greatly diminishing the binding of oxygen and facilitating oxygen unloading to actively respiring tissues.

How can oxygen be unloaded if the cavity is too small for 2,3 BPG to enter in the first place?
Or is this possible only when the hemoglobin is not fully oxygenated?

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