You can get a replacement from 3Rivers, or other sources. I would do that because you don't want to let moisture have free accesss to the inner core of th riser. If you don't put one in, or plug the hole somehow, at least seal the inside of the hole with some kind of glue as a moisture barrrier.
Why a stabalzer. They wer mostly used (and still are) on tournament bows, as a long rod (24" +) with a weight on the dnd. They really keep the bow hand from shaking or drifting.
Grab a door by the handle and try to move it. Pretty easy. Now grip the door by the hinged end and try to move it. Not so easy.
The extended weight of the stabeliser keeps the hand from "drifting off the target. Target archers will experiment with different lengths and end weights to find which setups work best for them on their particular bow.
Ben Pearson went a step further with stabalizers for their Lord Mercury bows. The weight at the end of the rod was a small barrel shape containing mercury. Different manufactorors came outh with their own versions. Bear came out with the "omni-coupler" which had a rubber bushing at the base of the stabelizer. This gave the rod mor flex. Now they have Y-bars that split into two rods with weights. Hoyt had their "torque flight compensators". All different marketing "gimmicks" but they pretty much all worked.
I don't know who did it, or when, but someone, probably Bear, came up with the bright idea of a four inch weight to screw into a hunting bow. If you look at the old catalogs you will see inserts on tournament bows starting around '64. You didn't see them standard on hunting bows until a few years later.
Bear used the inserts to market their Convert-a-quiver which used and adapter to mount the bottom of the quiver to the stabalizer hole. Then they came out with the screw in bowfishing reels instead of the tape on or spring arm reels.
I have an adapter that you screw into the hole and you can mount a standard spinning reel.
Most wheelie bow shooters use a variety of stablizers that are as varried as any of the other high tech gadgets they hang on.
Go to e8ay archery and search "stabelizer"and see what pops up.
Sorry to rant on so much...now you see why did't want to start this at 5:00 o'clock at work/
Bottom line...in my opinion...on a hunting bow...they are worthless. All they do is add dead weight to the bow, and without and extended rod, you wont get much stabelization
OK all you old knowledgeable experts...where did I go wrong.