The state from which they launched (presumably with permits) is fully responsible for the damages. I.e. if they allow smallcorp inc. to launch a tiny cubesat; if that cubesat hits something important and causes $1 billion in damages, then that country is liable for the full amount, no matter if they can recover that money from the (likely bankrupt) company or not.

https://en.wikipedia.org/wiki/Space_Liability_Convention