The human body will work until the last breath of oxygen is depleted.
I like that wording partly because that's how oxygen is brought into the body, generally speaking. Moreover, the word breath is sometimes used figuratively as well (as in breath of fresh air, or breath of a scandal, e.g.), so you needn't be overly concerned about using the word to mean a small, indeterminate amount, because there's precedent for that.
So, you wouldn't necessarily be referring to a literal last breath of oxygen – but you're not referring to a literal last drop of blood, either, so I assume that wouldn't be a problem.