Can liability Insurance cover you when hit by a stolen car?

Not usually. If you are trying to make a claim from the stolen car's owner, you likely won't get coverage. Most liability policies have an exclusion for 'intentional acts' or claims arising out of the criminal use of a vehicle, which would include if the car was stolen.

But if you have uninsured motorists coverage (many states require it), then you'll be covered anyway from your own policy and won't need to make a claim against the owner.

Also....you would likely have personal liability against the thief so you could try to collect against that person.