This takes that into account - you don't spend all of your money until you have no chance of living another year.

(In this case, the assumption is that you might make it to 111 but will not make it to 112, which is not completely true but very accurate.)

If you assume that you always have a decent chance of living one more year, and you're not bringing in additional income, you essentially need to maintain a floor of savings and just live off the interest.

However (and unfortunately), this is a bad assumption. You can show that by calculating the distribution of ages for a human population that has nontrivial survival rates; they don't look anything like the actual human population.

(Explicitly: the survival rate falls off exponentially or faster. In other words, if you don't like 112 as a maximum age, you can assume 125 - that's 2 years older than the longest-lived human being.)