I'm going through the soul cairn looking for notes to give to Jiub. However upon killing a boneman, his soul embers fell on top of a note and now I can't pick it up. So far I've waited a few days and exited and entered the cairn again but the embers are still there, on top of the note. Is there anything I can do, or will they just go by themselves eventually?

Yes, there is actually a workaround.

You need a Scroll of firestorm ***, and the Unrelenting Force shout.

Use the Scroll first then the shout.

*** Can be bought from the College of Winterhold

If you know the adept level alteration spell telekinesis, you can just pull it to you.