Who shares with us the fastest and needs constant updating? Bone marrow cells and epithelial cells of the skin and mucous membranes. In this regard, it is most reasonable to expect a trap from the bone marrow. Leukocytes live on average, presumably, for a couple of weeks, after which, in conditions of non-renewal of their pool, immunodeficiency quickly sets in - and "goodbye, cruel world" becomes only a matter of time. Platelets live for about 10 days, and the non-renewal of their pool threatens with the fact that for some time you can slowly bleed out due to various microdamages that a healthy person with normal platelets simply does not notice. A little faster you can reach the target state if you are injured with damage to some more or less large vessel: the thrombus is not eternal, the supply of clotting factors is not infinite, so sooner or later the thrombus will lyse, and the leak remains unsealed, well, the further question is again time.
Erythrocytes live 3-4 months, therefore, without their renewal, a person is guaranteed to die after this period. But until this happens, he will suffer from problems with the gastrointestinal tract, because intestinal cells live much less than erythrocytes (some - a little more than a day), and as they die, intestinal functions will weaken.
But a person can die in the early days. If you get a serious wound, it will not heal.
Therefore, I assume the following outcome: problems with the gastrointestinal tract begin in the first days, this leads to any damage to the intestines (which, in turn, cannot heal), and already from them a person dies. I think it won't last more than a few days.