Can another comic legally steal your joke? The answer annoys everyone.
Copyright protects the specific expression of a joke (the exact wording) but not the underlying idea or premise. That’s why two comics can riff on the same observation and neither is infringing. Even so, it takes more than changing the names involved or a few words here and there to avoid infringing the original writer’s rights.
In practice, the comedy world has long policed joke theft through reputation and community norms far more than through courtrooms. There was an even better system for policing in the days of Vaudeville, but that is a post for another day. These days, some comics are resorting to the courts to protect what they have created, as more material lives on video, where the exact expression is fixed and shareable.
If your livelihood depends on your material, there are real steps worth taking to document and protect it. Want the practical version of what actually helps if someone steals your set, or even just your best joke? Ask me and I’ll write it up.