Truthfully, I wouldn't try to bend the wire, you may break it farther down.
It could, but it hasn't happened to me yet. I've done the repair many times.
I think the wire develops a weak spot from repeated bending. Once there is a weak spot, that is where it will bend if you move the wire around. Bend it enough times, and it breaks.
Tin the end of the wire to connect to it and then just solder them together side by side.
I've tried to do the repair in this manner, and found it too difficult to hold the wires in alignment and steady.
I have put the two wires side by side, and wrapped them with another wire, such as a single strand taken from some stranded hook up wire. That works if you have room to get the wrapping wire on.
There is usually more than one way to make a repair.
