It's not unheard of for a herb or such to have opposite effects when taken in small doses versus large doses. As an anecdotal example (most examples for this sort of thing are probably anecdotal), white mulberries can make me more depressed if I eat a bunch, but if I just eat a few, they make me less depressed than had I not eaten any.
Or, it might treat the symptom while you're taking it, but cause the symptom after you stop, or treat it for a period of time and eventually cause it (even if you're still taking it). The same thing that can treat a problem can often cause the same problem. However, making it reliably do the same thing for every person is perhaps the hard part. If it's just one person's physiology, you may be in luck. People often respond differently to stuff that doesn't just intensify the effect based on dosage.
So, I think what you're asking is definitely possible. Getting a solid explanation for it and the science behind it might be tougher, though, if you need that.
It sounds like maybe an addictive substance with severe withdrawal symptoms may fit your need. The withdrawal symptoms might include death. You might need more of the drug (not a larger amount) to ease off of it over a period. This idea has probably been done before, just for the record. I know similar ones have been done.
As an alternative, you could have an essential nutrient. Extremely low doses of it could be fatal, while higher doses could be healthy.
Low doses of a substance might cause microbes/parasites to produce a toxin, while a higher dose might kill the parasites (thus evading their toxic reaction).