The Avo's Tear is one of the things that has fueled theories and conjecture for Fable fans for a long while. The problem is the source: Lionhead gave conflicting information about it on multiple occasions.
So. Let's start with Fable: TLC. The guy's name was Solcius, and he was apparently a really badass mage. He took a guard's sword to channel his whatever into stopping the vortex killing him and locking his energy in the sword and stuff. That story doesn't particularly appeal to me as you might have guessed, but it's the one most strongly supported in TLC, it's written in the in-game book A History of the Guild, Solcius stands proudly as a stone statue outside Maze's quarters, and Solcius is buried in one of the four graves at the guild, the fourth and emptier of which being the one that relinquishes the sword itself.
In Lionhead's Tales of Albion, which if I remember correctly was removed from their website some four years ago, Nostro commissioned the sword's creation modeled off of the Sword of Aeons while he was Guildmaster. I do not like this explanation at all. Not just because the idea that the guild had smiths that could duplicate the power of the Sword of Aeons, which none of them had even seen, is preposterous and conflicts with them being unable to duplicate the master weapons of the Old Kingdom, which are certainly newer and less powerful than the Sword of Aeons, but also because the rest of the source material is a steaming pile of dung.
In Fable 3, you can find Avo's Lamentation, which is stated to have been made at the same time as Avo's Tear but for some reason was lost for hundreds of years. And is apparently found roughly 550 years after it's twin. This poses a problem with both stories. Obviously the Solcius story requires that there only be the one sword, since the dude can only die once. And as impossible as it would have been for Nostro's people to make just one of these swords, it'd certainly be more impossible for them to make two, which has the added benefit of being trivial and pointless. My solution to making the Avo's Lamentation work in a canonical way is that a talented smith did make it, but it wasn't Solcius or Nostro or anyone who worked for either. More probable is that it was some guy who wanted to get rich and sold a ton of "legendary" weapons. Be sure to inspect it for a "Made in China" stamp somewhere.
Now, I've never, ever heard any story about William Black or any other Archon mass producing Avo's Tears and giving them to head guards. Obviously it conflicts with all the other stories, and makes no sense. If the elite guards had Avo's Tears, Solcius would hardly need to sacrifice himself to create one when he could instead just pick it up off the dead guard. So it conflicts with that story. Going back to the same point with the Nostro and Avo's Lamentation stories, Nostro certainly didn't need two so I don't think he'd have even more made. Where ever you heard that, though, might not be entirely incorrect. The Archons were around in the Old Kingdom. What did the Old Kingdom have? Old Kingdom weapons. Master weapons. What do the meanest toughest guards and bandits and even Jack of Blades himself all have? Master weapons. Maybe one of the Archons had a ton of these master weapons created and distributed. That certainly makes a lot more sense.
This is why the Solcius story is the only one that even remotely holds up. And, again, that's the one heavily supported in Fable TLC.