A recent question on poisons was answered in part by bringing up the concept of $\pu{LD_{50}}$ and animal testing and so on; none of that was new to me, but it did bring to mind a question I don’t know the answer to:
Has there ever been a substance that scientists have actively tried to determine $\pu{LD_{50}}$ for, and could not because they were unable to determine a dosage low enough to kill “just” half of the subjects?
Please note that this question is not restricted, strictly, to any technical definition of “poison.” Rather, answers must meet these requirements:
There must be research (considering that I am looking for something that might be a negative result and those do not get published as much as they should be, I won’t demand peer-reviewed publication, but the goal should have been to attempt peer-review publication if it had worked out—effectively, I mean serious work), and
that research must use the term “$\pu{LD_{50}}$” to characterize the substance.
Basically, I don’t want to get into debates about what is, or is not, a poison here. If a researcher is willing to call something $\pu{LD_{50}}$, then I am willing to accept it as a “poison” for the purposes of this question.
I also don’t want speculation, or for a user here to characterize something as $\pu{LD_{50}}$ when the underlying research doesn’t call it that. It is not enough to say, for example, “well I’m sure even a single atom of antimatter inside your body would be pretty bad,” you need to cite a particular researcher who has performed experiments with the goal of determining what they themselves called $\pu{LD_{50}}$ for that substance.
I suspect the answer is no, but I have no idea how to research something like this.