If there is something different biologically different about the 1,000th person, could it be tested for?
Drugs act on proteins which are little machines in the body, the instructions of which are encoded in our genome. The slight variations in our genetic code leads to some proteins having slight variations in their structure (and their function). Most of the time this is harmful, but sometimes it causes them to react differently when they interact with a drug or with each other. The manifestation of this can sometimes be harmful. Understanding "pharmacogenomic" effects will help us mitigate these side-effects going forward.
There are far more combinations and variations of the above variables and sub-variables than can be tested for in clinical trials. This fact means that some obscure combination of these variables may result in unintended negative (or positive, less frequently) consequences upon consumption.
Theoretically, you could test for differences in the 1000th person-- with today's technology, it would be a test which described the person's genome. Once scientists had that genomic data in hand, they'd certainly find a profile of alleles which could feasibly describe why a negative reaction occurred.
Importantly, everyone's genome is unique, meaning that a correlation between genomes and negative drug reactions must be exceptionally rigorous in order to be believable. Currently, this correlation poses a problem, as our ability to quantify and understand genomes is far ahead of the other dimensions which I mentioned at the start of my post. As our understanding of the microbiome, enteric connectome, and epigenetics increases, it'll be more possible to predict adverse drug reactions beforehand, assuming the patients in question have been profiled.