You can select live stream duration length before publishing it.
Continuous live on Facebook (longer than 8 hours) is available only for verified pages. You can double-check whether your page is eligible for continious streaming this way.
There is no limitations for Youtube stream duration. It can be live even for weeks if you need to.
If you want to stream a countdown that lasts for days, and your page is not verified, we suggest you to create separate streams with countdown clocks that last for 8 hours. For example: You want to stream a countdown that lasts 40 hours. In this case, you can create 5 separate streams, that are launched one after another and last for 8 hours each.
Continuous broadcasts (longer than 8 hours) won't be saved on the page after the end of live streaming. Once the broadcast ends, the post will be unpublished from the timeline, which means only the broadcast owner (page admins) will see it.