I've seen this affix on a couple of legendaries and I don't understand what the affix does. I mean, on Fire Walkers, there's trail of fire which actually does a little damage (I've seen this for myself). But what does "Slain enemies rest in pieces do?" I saw this answer for Diablo II. But as far as I know, there's no resurrection of dead monsters or anything like that (I play only a DH, so I don't really know about WDs).
When you kill something with an item with the "Slain enemies rest in pieces" legendary affix (like Sever, Boneshatter, or Last Breath) it seems that you get a large crit with your last hit (the killing blow), which might be useful if you have lifesteal.
This seems to work with debuffs like the DH's "Marked for Death" with the "Grim Reaper" rune. If a DH casts the debuff on a mob and someone w/o the legendary affix kills the mob, the crit effect on killing blow still happens.
This affix makes your last hit on a monster much more powerful (like a huge critical strike). But it does proc only when the monster would have died with a non-proc-hit. Consequently, it does not boost your killing speed. The main interest of it is a very large life steal at every proc (full healing for almost every single proc) and the Easter Egg about the "Slained enemies rest in peace" affix of Diablo II.
Edited based on spartacus comment.