Now that AI can seamlessly imitate a person's voice and likeness, this means our digital likeness is virtually immortal. If AI has access to enough of your conversation and writing, it can probably do a good job of impersonating your personality, too.
The default in copyright law is that everyone owns their own likeness. It's why you often see faces blurred out on TV. It means the production company didn't get the person to sign a model release form. However, the law is much less clear about likeness ownership after death. It varies by country and state, and generally gives much fewer rights to the individual.
Is it time to strengthen those laws? The thought of being the property of Big Tech in perpetuity is dystopian and depressing, even if you won't be around to experience it.