Sure, but false positives and false negatives are inevitable, since there's no indicator of death that can't be spoofed or missing. The best you can do is to reduce false positives by requiring very strong evidence of death (and very weak evidence of being alive), or a very long interval of presumed death. In a perfect world, perhaps you could tack on a public insurance fund for wrongfully being considered dead.

But in those cases, you get back to the issue of proving identity, since if you've been in a situation where you're presumed dead, you might not have anything left but your body. Also, such situations are rare enough that they'd be dwarfed by more mundane cases of others trying to claim the identities of the dead, so there would be net pressure to make proof-of-liveness more stringent.