So although tongue-in-cheek, it is an interesting question when dealing with medical records data (in particular I deal with insurance claims data in the US).

So to be clear, I know the person is alive when discharged (there is a code for death, as well as to hospice for example, in which you don't want to look at readmission either).

So a scenario in which someone is discharged, has a follow up heart attack, goes to ER and dies I would observe. The case the person dies and does not go to the hospital though I would not observe (no follow up insurance claim).

The latter scenario certainly happens -- how often it happens and how much it would bias my estimate in this case I am not sure.