We already know how mass vaccination of a leaky vaccine works.
https://en.m.wikipedia.org/wiki/Marek's_disease Because vaccination does not prevent infection with the virus, Marek's is still transmissible from vaccinated flocks to other birds, including the wild bird population. The first Marek's disease vaccine was introduced in 1970. The disease would cause mild paralysis, with the only identifiable lesions being in neural tissue. Mortality of chickens infected with Marek's disease was quite low. Decades after the first vaccine was introduced, current strains of Marek virus cause lymphoma formation on throughout the chicken's body and mortality rates have reached 100% in unvaccinated chickens. The Marek's disease vaccine is a leaky vaccine, which means that only the symptoms of the disease are prevented.[12] Infection of the host and the transmission of the virus are not inhibited by the vaccine. This contrasts with most other vaccines, where infection of the host is prevented. Under normal conditions, highly virulent strains of the virus are not selected. A highly virulent strain would kill the host before the virus would have an opportunity to transmit to other potential hosts and replicate. Thus, less virulent strains are selected. These strains are virulent enough to induce symptoms but not enough to kill the host, allowing further transmission. However, the leaky vaccine changes this evolutionary pressure and permits the evolution of highly virulent strains.[13] The vaccine's inability to prevent infection and transmission allows the spread of highly virulent strains among vaccinated chickens. The fitness of the more virulent strains is increased by the vaccine.
