I have noticed a rubber ring just before my swaybar bushing. The ring is badly damaged and needs replacing - however, I have no idea what it is called and thus cannot find a replacement.
That looks to be like a broken lateral swaybar lock. It's supposed to keep the sway bar from moving side-to-side through the bushing (so that its only motion is torsional).
You tend to see this in the aftermarket for increasing suspension performance, like here.