Brazing the broken piece back in place isn't likely going to work either.
I think what Carla was suggesting is brazing the hole closed, and building up braze to replace the broken part, then drilling a new hole for the pin. That will work, but it's not really the best way to do it...at least in my opinion after fixing several just like this.
Grind the end cap down so that you remove material just to the level of the pin hole. Get an appropriately sized washer that fits the outer diameter of the tail cap assembly by the pins. Open up the inside diameter of the washer to roughly that of the inside of the tail cap assembly. Braze, or better yet, TIG weld the washer in place.
Take the repaired tail cap assembly, put it in the body of the vise, insert the nut, and find something like a socket around the size of the nut, and mount the whole thing in a large vise or clamp (anything will work). That will have the body of the vise, the tail cap assembly, and the nut all lined up.
Drill the pin holes one size larger (stock was .250" for this size, so go up to 5/16") and make new pins using dowel pins cut to size.
Sorry...the pictures are somewhat out of order and actually from two different repairs. I also never took one after grinding down to the level of the pin holes, but without the washer. Still, you can get the idea. If you don't grind down to the level of the pin holes, there will be slop between the pins and the washer. I actually grind down a bit more than the pin holes because when you drill the new holes it will remove just enough material off the washer to keep things snug. This fix is literally stronger than new when you weld it, and more than strong enough when brazed.