There's a slight misunderstanding.

Let's call a disease Virus X. If a person gets vaccinated for virus X, then they will not catch X. Even if they are the only ones vaccinated, and everyone else is not, they will not catch Virus X.

However, as a virus lives on, and is transmitted, it begins to mutate, into Virus X2. A person who is vaccinated for Virus X can still potentially catch Virus X2 because they don't have the antibodies to protect themselves from it.

It's why they have a new flu vaccine every year. It's not for the same flu, it's for a different mutation of the flu.