So, there are three parts to this event. The third part is repeatable.
Part 1 starts when you pick up a mysterious gun outside Moxxi’s on Sanctuary III. It’s pretty weird looking, sort of alien in nature, but you can kind of tell it’s some sort of smaller armament like a pistol or SMG. It doesn’t have any identifying mark by any manufacturer or owner, but it does have a label pasted on it that says “PROTOTYPE - INCOMPLETE.” The latter part is definitely true, as it doesn’t even fire! For this mission, you have to go around to Sanctuary’s notable inhabitants and see if they know anything about it. Nobody does, and since there’s nobody who’s mentioned a missing gun at all, they conclude it must’ve been dropped by a drunken patron who’s probably halfway across the galaxy by now. They suggest you get into contact with representatives of all the different weapon manufacturers and try to get some sort of sweet reward for turning it in.
Part 2 of the mission is just that. You go to Pandora, Promethea, Athenas, and Eden-6 to locate and talk to representatives of all the weapon companies. All of them deny that the gun is associated with their respective company, but offer to “fix it up” for you… if you’ll do some work for them. Finding and talking to all of them unlocks Part 3.
In Part 3, you decide which weapons manufacturer you want to finish work on the prototype, imbuing it with their unique characteristics. In exchange, they send you to a new, event-exclusive planet to do a job for them. The map is a very well-planned city with a central district and a district for each of the manufacturers’ jobs. No matter what the job is, whether it’s a hit job, smuggling supplies, or otherwise, you’ll encounter resistance from the city’s security force (who definitely don’t want a Vault Hunter snooping around these parts!) and the mafiosos who secretly run the town. After you’ve done the task, you return to the representative and get your gun! No need to worry about a big galactic conglomerate having access to whatever freaky tech that gun held… right?
Repeats of the mission would start with you picking up another gun outside Moxxi’s (shhh, don’t question it), then jumping straight into Part 3.
The gun is a unique blue-rarity gun, either a pistol, or a SMG if manufactured by Hyperion (since apparently they don’t make pistols any more?). The gun, of course, primarily takes on the gimmick of the manufacturer, and its appearance changes likewise (although the main base of the gun is the same); for example, getting wood parts for a Jakobs, having an overhead barrel for Atlas, or getting all kinds of messed up for COV. However, the red text effect of the gun is always the same. I’m thinking it would be something cool like: Projectiles penetrate enemies and ricochet off objects in a random direction, dealing increased damage if they then hit an enemy, disappearing after some time. The gun would have decent stats all-around (again, depending on what would qualify as “good” for each manufacturer), and would always spawn with an anointment that would improve all stats by 20% after activating your action skill.
There would also be a handful of legendaries that could drop in the new event area.