Sounds like a story I once read, by Barry Malzberg. I don't recall the name of the story, but I recall it appeared in his collection "It Came From Schenectady".

Even if they are bound to obey the students, in this specific case, I would argue that the 'or something' part of the command acts as a sort of 'escape clause', allowing the elf to do something other that immediately go to sleep [and I imagine it would simply continue on with its normal chores at...

First counterpoint: Was it even Voldemort that cast the curse which killed Fawkes? To my recollection, Fawkes was killed by one of the Death Eaters chasing Hagrid/Harry, and it was only after Fawkes was recognized by them that Voldemort knew which 'Harry' was actually Harry, and came to him. Se...