After far too much wasted time on Wikipedia, I wound up at the statement that "in the process of forgetting, memories fragment and gist and verbatim traces can become independent." Time to revisit Augustine of Hippo, perhaps. The latter part of his Confessions address the relation between memory and identity.
This is of particular interest to me, as over the past four years I have witnessed my grandfather's descent through Alzheimer's. His physical sufferings came to an end in June.
I believe that ultimately, each person's identity is a mystery, known fully to God alone. This is why the Orthodox chant of "Memory eternal" at the death of a person resonates so deeply with me. Even as the body decays and the brain is eaten by worms, the full identity of that person is preserved in the love of God. In the eschaton, we will finally be revealed for who we really are, each person clad in the glory of God to the extent each has participated in it.