Twitch has introduced a new feature today that allows certain qualified on its service to stream exclusively to their channel's paid subscribers.
Simply called Subscriber Streams, this feature is available for Affiliates and Partners - aka, people who can receive paid subscriptions from viewers. The other requirement is that the person wanting to host the Subscriber Stream cannot have violated Twitch's Community Guidelines within 90 unique broadcast days, meaning they must have hosted a stream on 90 different days after receiving a suspension before they can host a Subscriber Stream.
Users who are not subscribed to a channel and who open a Subscriber Stream will see a preview of the stream, but will not be able to watch the full broadcast without paying to subscribe. Using the monthly "free" subscription awarded to Twitch Prime members works the same way any normal subscription works and allows access.
Following a stream, the streamer has allowed for VODs to be viewable, the VOD will be subscribers-only. Clips taken from a Subscriber Stream will be viewable by anyone unless the streamer indicates otherwise in settings.