I've never heard that top paracord piece called a "safety ring," .
I believe what he's referring to is the piece of cave line I have circled in this photo (it's a little hard to see). I recently within the past year added it to my stages. I have yet to use it thankfully. A friend who's an exceptionally accomplished instructor and explorer recommended it. It's basically there in case for some reason your upper attachment breaks, comes undone, or seizes closed. If any of those things occur you can use a double ender to secure the tank neck. I doubt I'll ever use it and it is probably unnecessary, but now that I've combined scootering with my rebreather I'm going much further back in the caves than I used to. It can't hurt to have a safety net even if it'll never get used. I don't really want to scooter back to the entrance for an hour holding up a tank neck. I don't believe they're very commonly used. I've only seen a handful of people use them.