Oh, one of those types.
And, seriously, you don't have to worry about expiration dates with a majority of pharmaceuticals, including most OTC NSAIDs (acetaminophen not being an NSAID, but still falls under the same group I'm describing).
To be fair, 100 years may be cutting it. But four, five, ten years past the date? Those bottled pills will be just fine.
If someone sick touches a pill and happens to be infectious material onto said pill, it's 99% likely said infectious material will be rendered dead/inert in a few days, tops. Only a few bugs can survive long term, but they generally need heating/cooling cycles and are rarely found outside of food-borne pathways.
And unless you've lived in a bubble your whole life, most of those more worrisome, spore-forming baddies aren't going to be able to form colonies inside said bottle, and thus your stomach - and more importantly, immune system - will be able to handle a single little bug.
In the end, if it's a major worry, YOU can dole out said pills from said bottle (if you're this into germophobia, you probably use hand sanitizer religiously, yes? if not, why the hell not?!). If giving pills to someone who is actually carrying an infection (or, you are worried they wiped their ass without washing, ran their hands through freshly manured soil, etc), whatever microbes you happen to have on your hands (sanitizer, stat!) will not make matters worse for the recipient, 99.99999% of the time.
Unless, of course, you frequently dole out pills to persons with HIV/AIDS/other immunodeficiency issue, or you yourself have such a condition. Then, by all means, practice and seek out the most germ-free way of life.