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Assuming you're talking about the Polio vaccine, that 1-in-100 stat is way off. It was never that bad.

The rollout for the Salk vaccine (the original polio vaccine) in the 1950’s was for 1.3 million children. It was probably the worst vaccine incident of all time because Cutter Laboratories, who produced roughly 200,000 of the doses, made defective batches that contained still living polio virus (and because of how vaccines are made now this is no longer an issue). Several thousand reported cases of polio, 200 permanent injured, and 10 dead.

Even if you were one of the unlucky people to specifically receive a defective vaccine, you still only had a 1/20000 chance of dying. If you look at the entire rollout then it was only 1/130000.

You're right about the 1-in-3 chance of dying from polio though, so even with it being one of the least effective and most dangerous vaccines ever mass produced it was still hailed as a massive success and won numerous people Nobel prizes.