Magic the Gathering question

So I had a deck idea I was making and I bumped into a thing I thought was confusing, so I'm running a low creature deck with 7 creatures, one being "Ulamog the infinite Gyre" and an enchantment "Shifting Shadow", my question is that "Shifting" has a death trigger that gives the creature an ability making it die on upkeep, which also allows you to reveal till you get another creature, but what if I have "Ulamog" enchanted onto it? Say if "Ulamog" was the only creature in the deck could it potentially be able to kill "Ulamog" have his ability trigger and than bring him back out as Shifting Shadow resolves just to re-enchant back onto him?