YouTube Content ID does run on live events just like any content uploaded to YouTube. So if your live event contains copyrighted content or content that violates YouTube's community guidelines, your live event will be subject to the same restrictions as any other YouTube video. Privacy settings don't matter. Meaning, if you are doing a test event set to private, you still can't use that TV show as a video source.
If you continue to stream that content, your event will be stopped automatically and live will be disabled on your channel. You will see a message in your video manager letting you know how long it will be until live is re-enabled.
How do you prevent this?
1- Make sure you work with the content owners to ensure you have the proper rights for all content you include in your live events (even private ones and tests).
2- Pay attention to the Live Control Room during the event and follow the instructions if you get a warning.
3- If you receive a copyright strike, visit the YouTube Copyright Center for more information on how to resolve the issue.