You can receive fragments of ninjas in Elite instance. But it is random. For example you can't receive all ninjas this way, you can only get fragments of ninjas you met/fighted in story (and even after that it is not every single ninja).

I thought that in the way the number of day, give me the ninja in question, in the end, the time indicated is not taken into account.

Never mind my previous comment please.

I have mistaken Survival trial with Elite instance xD.

------

Back to your question - it drop rate of ninja fragments is random. But you can do each of them only 3 times per day.

I think I found. The time shown is for the remaining time, only if we drop 3 fragment of a sudden, during a sweep. Example, after winning 26 fragment in the proceeding, it will take 18 day a sweep if we harvest 3 fragments every time, has more long otherwise.