Basically, when you have a treatment (a 'leaky vaccine') that prevents symptoms but not transmission, then the normal evolutionary constraint for a virus to become less-harmful (to maximize transmission) goes out the window - because anyone that's been vaccinated could just as easily carry a more-harmful version of the virus.
It doesn't always happen, and it's hard to predict when it will, but Marek's disease is an example of a worst-case scenario actually happening: when a leaky vaccine scenario allows the virus to mutate and become highly lethal.