I have seen jade swords with rings along the back before. They are tourist items so the function and balance is not worth examining.
I can't find a picture of such a sword on e-bay now, but you can find all sorts or jade swords and jade blades or hilts being sold. They are all modern and are fantasy items.
As far as the purpose of rings and such it might be better to ask the question in the martial arts forum or start a thread so somebody notices who studies later weapons.
It is not meant to make an injury anyway, or disembowel. Dao are slashing swords and you won't be thrusting a sword like that inside somebody up to the hilt. Even in thrusting swords you dont really want to get the blade stuck in the opponent.
In the early bronze thrusting swords often the last 1/3 or so of the blade was waisted/narrowed, and like with the Roman gladius it seems you only need the last several inches to make a lethal wound.
Jade was used for weapon forms from neolithic times, but these were (IMO) ritual or symbolic version of the real thing. Like many other jades considered ritual pieces they are slender and finer versions to be held by ranking individuals and not for clobbering people.
There are jade spears and some archaic jade ge (dagger axes) from Shang and Erlitou culture sites. These are also likely ritual versions of what were by then real weapons made in bronze.
Just as the real Shang items are mostly from thin sawn slabs if you have large or heavy jades then they are invariably modern, excluding the possesions of Imperial families.
I have seen some really really bizzare jade swords being sold that the new owners assured me were Zhou and argued at length, but any jade sword sold via antique dealers will be fake whether they face it or not. These 'Zhou' swords were said to be from Xian, but even at a glance one was based on an Indian Rajput sword from the 18th century, and another clearly a blade like a Kukris/Gurkha knife. They were all just fantasy pieces, with animal heads and wierd shapes.
A late dynasty dao in jade will be a modern carved 'jade', using high speed tools....and likely an imported material and in all probability a jade-like stone in the broad sense (perhaps not even nephrite).
i.e here is a massed produced fantasy type. At least 3 people on the web are selling this same sword. This version here, one seller claims, dates from the stone age.