Here I am talking in general terms, for any pathogen, measles, flu, etc.
Regardless of the specific pathogen, as mentioned above, in general vaccines are not 100%/absolute protective. They are certainly on average more protective than no vaccine - this is what is demonstrated in clinical trials with rigorous experimental design (controlled, randomized, replicated).
That’s why some people may still be at risk, but especially people with certain conditions and older people who, as we know, have weaker immune systems. For measles, my understanding is that younger people are more vulnerable, relative to the general population.