There are 7 Daedric quests. You are tasked with the next one when you report in with Nocturnal. Once all are complete, when you report in, the following occurs...
If you report in on time, and as a virgin - No punishment occurs as usual. Since there's no Daedric to assign, all that happens is your counter for days to report in is reset, and you are sent off with your status unchanged
If you report in either late or with lost virginity (or both) - The usual punishments occur. Then you see a pop-up message "There are no more Daedrics to earn trust with. Nocturnal will give you freedom in a day or so. You will receive a notification when it's time.". This will allow you to get your needed rebirth as usual, without completing a Daedric quest. A "day or so" is actually randomly selected game hours between 20 and 30