Can you measure the depth of the pit? Pretty had to do. running around, usually means it's following a weld in the damascus - which can lead to a catostrophic failure. the 'rot' can run underneath the surface, following further than what's visual. I am not an expert on this. I have inspected many damascus barrels with similar defects and sectioned some as well. It is generally not very pretty and can be very bad as to continuous errosion and cracking. As to using an epoxy to 'fix' it, doubt it, but woth a try - maybe - can't say either way.

Since it's a rifle and the damage is on the neck of the chamber, going as oversize (reaming) as necessary in that area, then beafing up the brass (appropriate size tubing soldered into or onto the cases - then expanded and turned) to fit for bullet seating is probably what I'd end up doing, if it was mine and worth salvaging. Might try some form of epoxy first, though, just in case it worked.

In the reaming scenario, you'd have brass for left and right chambers - non interchangable.

In the epoxy scenario, you might have to re-do the epoxy often, or you could shoot mainly the left barrel, saving the right for an "if needed", second shot during hunting with the piece - probably the best thing to do anyway.

Of course, all of this depends on the severity of the material loss. Without more information, it's all guess-work.

I'd clean the hell out of it andonce it's shootable, shoot it to see how much they are sticking or if they are sticking. I'd not shoot it with the forend on it, if possible, until it was proven that the barrel wasn't going to blow apart at the neck. Does the crack run around onto the bottom of the chamber or is it the top 1/2 of the barrel?