When does a person actually stop being the same person?

I started this thinking about AI versions of people, memory, personality, etc. but the more I think about it, that might not even be the core issue. Like take extreme cases: paralysis, brain damage, personality change, memory loss...at what point do we actually say “this is no longer the same person”? Is it memory? Behavior? Continuity of experience? Something else? Feels like unless we understand that first, anything we build later is just guessing...curious how people here think about that...