Why are health authorities concerned when the vaccination rates for an infectious disease fall?

When the propagation of an infectious disease gets reduced, people stop getting their children or themselves getting vaccinated for the infectious disease.

But what we forget is somebody out there might be an asymptomatic carrier of the disease and can spread the disease. As a result, if many people are not vaccinated for the particular disease, then there might be an outbreak of the infectious disease again and it can be deadly.