The title of this thread Elimination rengo and the mention of rengo made me imagine it would be something like capture go where the players got eliminated when their stones got captured 
That’s not what the thread is about though.
So maybe one could think of capture rengo where the player resigns if they were the player who played the move previous to the capture.
I think having multiple “lives” essentially given the players, is an interesting idea, meaning some kind of ko capture can still be dangerous for the person to make the first capture