The pertussis vaccine is also a subunit vaccine. You can't get measles from the MMR vaccine although very, very rarely children can develop a viral meningitis from it.
Generally speaking, there is almost no chance of a healthy person developing a disease as a result of a live, attenuated virus vaccination. If you are HIV+, are pregnant, or suffer from a immunological disorder then you should be concerned about live virus vaccines.
When people talk about live virus vaccines, these are versions of the pathogenic virus that have been changed or allowed to mutate so that they are not capable of causing the original disease anymore.
If a vaccine is made from killed virus/bacteria, you cannot contract a disease from the vaccine.