I'm a physicalist, so I do not believe that mentality/consciousness and body are at all separate.

The person still exists in a limited sense when dead. But they don't have philosophical "personhood" any longer, since that requires sentience, among other things, which requires a brain functioning in ways that it no longer functions once someone is dead.

If someone isn't functioning just for a minute, they might not be dead per the medical definition (which is the definition I also use), because that requires irreversible cessation of brain function, repiratory function, etc. Cessation of brain function etc. can be reversible in some cases after a minute. It depends on the state of the body, just what's been damaged (for example, in an accident).

The boundary between that person existing in some sense and no longer existing is fuzzy, because the decay of the body is so gradual and ultimately fuzzy.

Given my view on this, people definitely continue to exist while in a vegetative state.

I think when a person is no longer conscious they are absent from us.

I feel a lot of important human communication is done through language which gives us an insight into another person and their inner world.

The loss of consciousness seems to deprive us of that person. I am not sure that what is being lost is simply a functional state. Also consciousness appears to be the seat of values and subjectivity.