If you have set your live streams to record - they are saved as videos that you can watch later (video on demand or VOD).
(Note: If you are live streaming when you turn this on - only subsequent streams will be recorded).
How can you retrieve these streams? You can use the list all videos endpoint. if you append liveStreamId={livestreamid} as a query parameter in the url, the result will be your recorded livestreams.
You can see this in action at the watch.a.video/broadcasting demo - and the code is NodeJS and available on Github