I guess this depends on your definition of "100% safely", and probably also on your definition of "drugs". Let's assume that "drugs" means "psychoactive drugs". In that case, I'd suggest that you can take a cup of coffee pretty much as close to 100% safely as is achievable for anything in the world that you can ingest. And coffee is psychoactive. So, it is possible to take drugs 100% safely.
Even alcohol can be taken safely: so long as you keep the dose low, and you're not someone with a special sensitivity to it (e.g. an alcoholic), you can have a glass of red wine with pretty much zero chance of anything bad happening.
That also applies to all the other psychoactive drugs in between: speed, cocaine, LSD, heroin, mushrooms, peyote, MDMA, whatever. They can all be taken 100% safely. The key in all cases is always the same: good education and moderation.
All of these drugs can also be abused. You can kill yourself with caffeine too (though unlikely in coffee form - you'd need about 50-100 espresso shots). I recall a story of someone who ate a whole pack of caffeinated candy, thinking it was normal candy, and died.
Shit happens.
Shit happens more often without good research, education and clear guidelines.
Shit happens even more often without good research, education and clear guidelines, and with dodgy suppliers who may or may not be selling you the thing you think you're buying because they're all criminals.
The real culprit in every drug death? The three branches of the government, who have failed to do the right thing on this topic for 50+ years now.
More powerful psychoactives can make education and moderation moot. Then the addictive qualities can drive the user down a well-trodden road. Ignore this at your peril.
I think that"100% safe" is an exaggeration intended to emphasize that the risk is manageable and it would be more polite to simply state that many substances can be ingested with minimal risk.