I have never seen written rules for ring games.
Just the general rules apply.
...
Here is how I remember we used to play....
The Rules of Ring Nine Ball
Ring nine ball is played by 3 or more players shooting in turn. The game is governed by the standard rules of nine ball with the following exceptions:
Spotting balls: Any ball made on a foul shot or jumped off the table is spotted.
Cue ball on a scratch: The cue ball is in hand behind the line after a scratch or if it's jumped off the table. If the lowest ball is behind the line, the shooter may have it spotted.
Fair try required: No safeties are permitted. The shooter must attempt to hit the lowest ball on the table. If it is agreed by all that it is not possible to hit the lowest ball, the player may push out.
Pass back: After any foul, the incoming player may pass the shot back to the fouler.
Optional pass-around rule: After a foul, each player in turn may pass the shot or take it with the shot going back to the fouler if all other players pass the shot.
Breaker: Winner breaks.
Change the order: Any player may request a re-draw for the order at the start of a game but the old order is used for that game. After that game is finished, there is a new draw for order with the winner of that game being first automatically.
Three player order rotation option: If there are only three players in the game, the order changes every rack with the person who sold out racking and shooting second.
Also, I think it's probably better to play "all fouls" in a ring game. That avoids some complications.