You cannot have a death certificate without a body. If a person just vanished, anywhere, no death certificate would be issued unless he/she had been legally declared dead. This would only happen if an accident had had to be investigated or a relative had applied (after seven years disappearance I think) for the person to be "declared dead" to tie up some legal matter. For instance "Missing, presumed killed" during wartime would have to be declared as a definite death in court for inheritance matters to be settled - so it is possible to have cases where no death certificate can be found. I know a case where a young woman simply vanished into thin air in the lat year of WW2 - she was gone one morning and no trace of her was ever found. Her family never had her "declared dead" and when her sister died recently a close friend of hers was astonished when I mentioned the sister who disappeared - she had never heard a word about it in years of friendship, so no one will ever be able to find out when, how or whether (probably dead by now anyway!) she died or went off elsewhere for some unknown reason. It can happen.