Ok, Ive searched the web for someone with a similiar problem, and it seems only I have encountred this bug.

Here is the deal; Hercine quest --> I kill stag --> I accept to kill the werewolf --> I go to cave --> decide not to help him kill the other hunters --> kill him after he have killed all other hunters --> skin him --> Go out of cave and nothing happens. No hircine.

Tried several times. Anyone know a fix?

That's it. That's the whole quest.
Hircine should speak to you when you kill what's-his-name telling you to take his skin.
If you wanted both items, I think you need to side with dog-boy in dialog then kill him after the hunters are dead or somesuch.

I think his problem is rather that Hircine isn't showing up at all. No matter what side you pick, he should show up (either to tell you to skin the dude, or to un-curse the ring).

Maybe I misunderstand, then. OP makes it sound as though he did indeed get the skin... ? Is it made into the Savior's Hide later? I guess I could just look it up.

Okay. Reading the wiki's, it looks like OP is trying for both artifacts. You'll need to side with Sinding first.
See http://www.uesp.net/wiki/Skyrim:Ill_Met_By_Moonlight#Two_rewards and http://elderscrolls.wikia.com/wiki/Ill_Met_By_Moonlight#Walkthrough

Wrong, I am not trying out for both artifacts, only the skin, and hircine does indeed not show up at all! That is why it's so damn annoying

Go back in the cave? I thought Hircine talked to you by Sinding's body, not out side the cave.

He does not talk to me anywhere Went outside, went inside again, outside again, nothing happens.

Have you tried reverting to a save prior to doing the quest and retrying the quest?

Often quest stages get "stuck" and don't advance so you're left with two options: revert to a previous save before the quest and try again or use console commands to advance the quest (provided you're playing on PC).

From past experiences, hircine should talk to you outside the cave. You could just reload and skin him all the way; don;t kill the hunters at all. Perhaps thats what caused your disappearing hircine.

The quest works well for me.

The quest worked for me. Went into the cave- I talk whoever I help or kill I went for the kill,- helped the hunters to kill the werewolf-(I was at level 10 or a bit later) hircine the stag appeared after I killed the werewolf-tell me to skin werewolf-I have the hide-stag gone.