Looking at it from a story perspective, it sort of makes sense.
Spider's Bane was an item found in BG1, correct? If memory serves, you find it in the spider-infested region of the Cloakwoods. Two wannabe adventurer brothers find it and, thinking themselves invincible, set off to exterminate the spiders and become heroes. One of the brothers, and Spider's Bane, gets poisoned and is dragged off by the spiders. The surviving brother begs you to go save him. When you finally find him, he's dead and Spider's Bane is now yours. So Spider's Bane would become the main character's property...
...flash forward to Baldur's Gate 2. Traveling from Baldur's Gate, the party is ambushed by Irenicus, yadda yadda. The party's gear is nowhere to be found in Irenicus' Dungeon (with a few exceptions, like the Golden Pantaloons, Sword of Chaos, Claw of Kazgaroth... and so on.) So, logically, Irenicus might have sold Spider's Bane to a retailler in Athkatla (Or had Bodhi sell it, more likely.) In this case, the merchant's goods might've made their way to the Cowled Wizards in any number of ways. From the Cowled Wizards it could be passed on to the Amnian government... and the two boneheaded workers don't actually own the sword; they have it on loan. From the guard- I think. This does not, however, explain how it got broken, unless one of the Cowled Wizards did it by accident with a Disintegrate spell.
Or maybe the workers really do break it, hitting it against the wall, or something stupid like that. I forget, because I did the quest a while ago. -_-'' But when I did it, they never actually gave me the sword (I [paid for it and got experience for getting it, and got a journal entry about it... but never got it), and so Pai'Na never let me finish the quest. So I lifted Kithkix off her via Jan Jansen. Not the most elegant solution, but hey...