The wire on my recliner runs through a hole on the bar that usually clicks into the toothed mechanism. The other two ends on the wire bend and fit into the U shaped metal bracket that is in the middle of a square rod that runs side to side under the chair. The wire is bent on both ends to a right angle with the ends long enough to cross in the middle of the U shaped bracket. Loosen the single screw enough so that the ends of the wire will slide under the screw. Then retighten the screw. If the wire has broken, save all of the wire so you can make a pattern from it and reinstall the new one, using the same gauge and type wire. I've done this two or three times over the years and it works.
Love my Lazy Boy
March 2009