In history, when the blade of the sword was damaged, was it usually reforged or were there other possibilities of fixing it?
A combination of superglue and duct tape?
But seriously yes if it was broken you could possible reforge it, but you’d have to keep in mind some (read most) swords were heat treated so you’d probably have to go through the whole procedure again to make sure you didn’t create a structural weak point.
Another thing that I think might have happened (just speculation though) is that if part of the tip was broken off (top 1/4 or 1/3) They could simply forge or grind a new tip on the remnant and shorten the hilt a bit to make a long sword a one handed sword. Not an elegant solution and it probably resulted in a somewhat poor handling sword but it might just recoup some of your losses.