As a T1, I'm wary about venturing into a T2 question, but I'm an inquisitive little fecker so will do so anyway!
As other posters have correctly pointed out, you would be dead long before your blood sugar reached zero.
The easy question to ask is why would you want to have a zero blood sugar, but the fact you've even asked a question about zeroing suggests to me the answer is that you've seen a huge number of posts here more or less demonising carbs, their effect on readings, and concluded that it's logical to zero it.
I take my hat off to you guys/gals who do keto, lchf, fasting: each to their own and all that. Those options do seem to work very well for T2s. Indeed, as a T1, I occasionally end up as an accidental low carber: who could complain about some griilled lamb chops and asparagus? Still have my omelette on toast, though!
But the thing which concerns me a bit is that when a new poster signs up, whether they're T1, T2, or some of the other wonderful variations on those themes, the overwhelming response is often a screed of posts that, "ok, mate, just do lchf, and you'll be fine."
That might be perfectly correct for T2s, but two problems:
First, the OP seems to have interpreted that as meaning carbs are so bad, so evil, that he/she is starving to try to zero. Serious misunderstanding of basic body chemistry going on there which could result in death. Should the lchf crew qualify their advice to make it clear that there's a difference between what carbs you eat, and what glucose is in your stream? The demonising of carbs which any reader of this site has seen blurs the difference.
Second, as I've said above, I'm an occasional low carber, but I recall when I was first dx'd and told I'll need several injections each day for the rest of my life, that was a bit of a head-f*ck on it's own, and it would have put me over the edge if I was then told that, by the way, I can never eat any carbs again. Yet, I've seen a fair few posts here immediately recommending an lchf diet to newly dx'd T1s, from T2s! Lchf is a choice we can all make further down the line, but I'm not sure it's proper to suggest it to a newly dx'd T1 when they've got enough to get their head round already.