Nessie once bubbled...
The worst I have seen was a solo-diver who had nobody at the surface, no buddy underwater and had attached his rope with a nail into the ice.
Wow...that's amazing.
We're safe. The line is attached to a D-Ring (Either on your BC or a harness), and you also have a loop that you keep your hand in to ensure that you have a good hold on the rope if your carabiner or know fail on your BC. Everyone has someone tending the line, and we have a safety diver that is sitting in the hole all set to go at a moments notice.
In addition to that, our ropes are attached to 6" titanium ice screws in the ice.
I'm not sure what else we could do to make it much safer - it's pretty much everything I learned in the PADI ice class.