I have a skeleton body outfit that is equipped as clothing for a dying vampire effect, but sometimes it seems to equip the clothing or maybe it was armor the character was wearing when they die. The skeleton outfit uses the upper body, lower body, hand and foot in the CS, yet sometimes other clothing / armor shows up equipped at the same time!

Is there a nif setting that is making it think this outfit is skin and not clothing/armor?

Sometimes it works, other times it doesn't.

I'm beginning to think, having had the same issues, that it's a variant of the companion Double-Face bug that happens when you fast travel. The same spell to fix the face seems to fix the double outfit issues for me. Can you confirm that you're seeing it happen after fast travel?

What spell is this?

Its possible. I've never seen the bug immediately, its always later when I come back, possibly after a fast travel.

It's bundled in UOP as a lesser power called "Fix follower double-face bug". I haven't opened it up to see exactly what it does, I just use it when applicable.