In Rinne, Rokudou uses a special Haori called "Haori of the Underworld" that grants several powers, like making a physical entity behave as a spiritual one, or vice versa (by donning it inside-out).
It is also a very precious item to Rokudou Rinne, more even than his Shinigami Scythe. This is evident during his duel with his father (wielding the blood-sucker fire wheel) when he threatens to convert the Haori into money.
He is half-shinigami and half-human, so he should have some powers (he can see spirits even without the Haori, but it is shown that anyone that eats afterlife food can do it, like Sakura).
What would happen if the Haori becomes permanently unavailable (stole, destroyed, etc)?