system
A chat on subreddit /r/NoStupidQuestions
human
Most vaccines contain zero virus, especially modern ones.  

Some vaccines contain some deactivated virus, and in theory there is a small chance.
gpt
A few contain *attenuated* virus, which is alive but modified to be harmless. The most famous one of those is oral polio vaccine. There’s a potential benefit: someone can spread the attenuated virus and immunize more people.

There’s also a downside: the virus can mutate back to the normal, dangerous form. That’s why live polio vaccine is no longer recommended in the US, although other countries still use it, usually along with a first dose of inactivated polio vaccine, which contains no live virus and can’t infect or spread.

And obligatory note: some vaccines are against bacteria, not viruses, and the question doesn’t even make sense. There are no live bacteria vaccines.