Kay truss rods are not an exceptionally great design, they use the basic compression rod system that Gibson patented in the 1920s but Kay fell short in their execution.
Gibson used a concave channel for the rod to follow in order for the compression to effectively counteract the forward bow in a guitar's neck. Kay used a nearly flat channel which makes the compression rod have a minor effect but its not always consistent down the neck. Often a Kay truss rod will bow the neck around the 3rd or 5th fret and leave the rest of it untouched. I opt to replace these rods with modern steel truss rods from LMII which perform miles above the original rods and are stronger.
The rod is a long carriage bolt that extends from the nut to just before the neck meets the body. It is held in place by two semi-circle washers with square holes cut in them. The adjustment nut is brass and sized for a 5/16" socket. It bears against a washer and the first semi-circle washer. Tightening the nut pulls the end of the rod towards the nut which bows it and is the basis of the functionality.
The washer at the nut is not attached to the rod but the washer at the far end is held in place by the resistance of the carriage bolt's square-neck against the square channel in the washer. This keeps the rod from turning freely when you try to tighten the adjustment nut.
My Kay truss rod turns freely, how do I fix this?
Using a pair of needle nose pliers, grab the brass adjustment nut (while it is attached to the rod) and give it a gentle wiggle. You should be able to push and pull the rod and have it move about an 1/8" overall. Pull the rod and give it a gentle twist to see if it moves. If the rod turns then the square neck of the bolt has not met the washer and I would recommend repeating the process. If the rod does not turn then you should be able to tighten the adjustment nut and your truss rod will work again.
The worst case scenario is that your rod is actually broken in which case you won't be able to fix it and it will need replacing. The best case scenario is that you prolong the life of this (admittedly poor) OEM truss rod and the minimal adjustment it provides.