What would happen if the aggressor stopped chasing the lateral mover?

Lets say for instance, in the Lara vs Alvarez fight or in the Garcia vs Peterson, what wouldve happen if Garcia and Alvarez wouldve stopped chasing Peterson and Lara and walked to the center of the ring? There was a point in the Garcia vs Peterson fight where Garcia stopped and waved peterson over to him but eventually went back to playing cat and mouse. But what wouldve happened if Garcia wouldve just stood there and refused to give chase?? Ive always have been curious about this because I dont think its illegal for a fighter to just walk into the center of the ring as long as he is protecting himself. And there is nothing in the rule book that says one fighter MUST be the aggressor at all times while the other one can move. Any examples of lateral movers being forced to fight in the center of the ring???