Ah, that isn't how a live vaccine works though. They get attenuated (aka damaged/killed/broken) or similar but not the same viruses (aka cowpox used to be a live vaccine for smallpox), then introduced. The body reacts to the not-really-functional virus, but it isn't the same as if it was an actual infection.

It still triggers the immune system, but mutations in any of the major receptors or the like will cause it to be less effective too.