Operational concerns might push you otherwise, but I think in terms of correctly representing the world what makes the most sense is a separate table of deaths with a primary key that's also a foreign key into the table of people, and which has a nullable date of death. That lets you represent all three of "they are living", "they are dead but we don't know when they died", and "they are dead and we know when they died".
If your table is expected to answer "how many dead people whose date of death is unknown" then you'll most certainly also need an "IsDead" (true/false) NOT NULL column. (Best separate the table into "Death" with NOT NULL DateofDeath.)