There is a philosophical (in the popular sense of the word--professional philosophers don't tend to defend this) outlook on death that says that we live on in people's memories of us. I was discussing this view with students in my Death and Afterlife class, and one of them connected this to the memory theory of personal identity. My first reaction was that this was completely confused. But after reflection, I thought that there was a deep point about the memory theory of personal identity there.
Start by observing how unsatisfying this kind of "afterlife" in people's memories is--it's not really "living on". Now, the student's potential confusion was that on canonical versions of the memory theory of personal identity, we live on through a chain of first-person memories, while the memories through which we are said to live on are third-person ones. But does that point matter? Suppose one or more of the people through whose memories I was said to live on actually managed to acquire first-person (apparent) episodic memory of my life, say by thinking about me so much. That's a bit creepy, but it's no more satisfying as an afterlife than when the memories were third-person.
Of course the proponent of the memory theory can say I am unfair. The memory theory requires that there be only a single person with those memories, and it has restrictions on what sort of causal chain is allowed to pass the memories on. But these matters of detail do not, I think, affect whether I am living on in any robust sense through a person who has memories of my life.