The brain is constantly evicting, shifting, and changing memories as new stimuli come in and change the connectivity of our neurons. In that sense the brain, from inception, is full in the same sense that in an artificial neural network every neuron has a weight. The only thing that changes are the weights. (Note that I realize ANNs are a dramatically overly simplified representation of the brain, but the point remains).
The brain may also choose to re-encode a memory as part of a recognized pattern, in a sense, finding a way of compressing memories as recognizing them as part of a kind.
