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I recall a story along these lines from Analog/Asimov, which has stayed with me for decades. People's health in the story is maintained in large part by nanobots. The story is of an elderly couple whose health is waning, and they are reminiscing about the past and deciding their ultimate fates. The wife, whose health is in the "yellow" and dipping into "red", has made up her mind that she will not have her consciousness preserved, because she doesn't think it will be 'her' in the same sense and she considers life to be special. She dies a peaceful death and is mourned by her husband.
As the husband's health wanes, he decides to have his consciousness downloaded. This is something that only the terminally ill are allowed to do, because duplication of consciousness is forbidden for ethical reasons, and is performed only to facilitate a very specific purpose. He's hooked up to the various probes in the medical facility and asked prompted questions to stimulate memories and parts of his brain, and these patterns are recorded and become his digital consciousness. He's asked to "think of something blue" and visualizes a blue rabbit plush from his childhood. Once the recording is complete, he is euthanized.
This story takes place in an era of interstellar exploration. However, faster than light travel does not exist, so instead of sending people to their deaths unnecessarily, autonomous essentially-immortal androids are shot into space on centuries-long trajectories to perform preliminary assessments and signal the results back to Earth. The androids contain the consciousnesses of dozens of individuals who have had consciousness uploaded, as one collective consciousness. The last part of the story is of one of these androids, floating through space on its centuries-long course, that has a random thought pop into its mind, the image of a blue plush rabbit. It acknowledges but does not understand the significance of this thought.