"How on earth does that work? Does the insurance company go broke and BP isn't on the hook for anything? Crazy."
Whichever party is legally at fault (presumably BP as opposed to their sub-contractors but I dont know) is liable. Its up to that (liable) party to re-claim from their insurer.
If the insurer goes broke thats the problem of the party which is legally liable for the problem in the first place.
Then there is the the question of re-insurance....
