By opening one link. The jeweller cuts through the seam of a single link, lifts the unwanted run away, threads the cut link through its new neighbour with the same half turn as the rest, and closes the seam with solder.
Because every link is the same and there is no sequence to preserve, the cut can be made at either end or in the middle. The bevel on the repaired link is touched in afterwards so it matches its neighbours.
A hollow curb is worked with more care, since each link is a pressed tube with a thinner seam, but the method is identical. Lengthening is done the same way in reverse, with links of matching width and finish threaded in.