There is a spectrum of brokenness - from the tiniest sliver of metal knocked off the sword's edge, to complete atomisation. There is, conceptually, a stage where the prior form (that of a sword - assuming some kind of linear comprehension of time) is no longer recognisable. That stage is, in itself, a spectrum depending on the observer's understanding of swords and the ability to analyse the parts.
Some questions:
If the only person observing the sword knows nothing of swords, is it still a sword?
If the sword has an imperceptible hairline fracture in it, is it still a sword - or a broken sword? Is it a broken sword only when you know of the break? Clearly the sword is broken, but there's no-one to observe it in that state.
What you come to realise is that "sword" is a convenient and simple, but imperfect and subjective, description of a thing. Brokenness is similarly a convenient and simple, but imperfect and subjective, description of a state of a thing.
The interesting part is when one person sees a sword, and another sees a plough and they talk about it.
"Sword" is an opinion. "Broken" is an opinion. People with opinions go around bothering each other.