This article presents conditions under which the skewed version of immaculate noncommutative symmetric functions are nonzero. The work is motivated by the quest to determine when the matrix definition of a skew immaculate function aligns with the Hopf algberaic definition. We describe a necessary condition for a skew immaculate function to include a non-zero term, as well as a sufficient condition for there to be at least one non-zero term that survives any cancellation. We bring in several classical theorems such as the Pigeonhole Principle from combinatorics and Hall's Matching Theorem from graph theory to prove our theorems.