"Unbreakable" in this context only means you won't lose it permanently. The one WCV's anti-magic cloth things that Ramirez chopped up are mentioned in the rulebook as being a case where Ramirez "breaking" them would likely be treated as a compel/maneuver, and (had he not been killed in the fight) he'd have gotten them back later, barring the whole 'determined ritual' thing.