When my mom died, people sometimes told me that she would "continue to live in our memories". That sounded like a load of crap to me. She was dead and gone, and pretending that she still existed just because we remembered her was false comfort.
Today I had some different thoughts on the matter.
They start with a question of the nature of self: are we each distinct, separate, isolated beings? Or are we an expression of the ecosystem, and our relationships with the rest of the universe? For as long as I can remember, I've had the first perspective, but since reading The Ascent of Humanity I'm asking myself if the second makes more sense.
In the first, Mom was contained exactly within her body. She ended at the "skin boundary". Everything inside was her, and everything outside was Other. Or maybe her body was just a host, and her Self is some mote that is hosted inside the body. I'm not sure, but I was sure that the Self is complete contained within the body.
In the second, Mom is the expressions of the ecosystem that created and grew her (her parents, her food, her intestinal microflora, the air she breathed, the people and animals she loved, the woods she walked in). That includes our memories and thoughts of her. When she died, the body began to decompose, and our memories changed to incorporate that knowledge, but all the "outside the body" aspects of Mom continued to exist.
In the second, perhaps we would say that her existence was largely diminished by her death, but not eliminated.