There might be a loophole the size of a mack truck, but nobody is taking action.
The US Congress passed the “National Childhood Vaccine Injury Act” (NCVIA) in 1986, which was to "leave judgments about vaccine design to the FDA and the National Vaccine Program rather than juries," ~ Justice Antonin Scalia wrote
No Vaccine manufacturer shall be liable in a civil action for damages arising from a vaccine-related injury or death associated with the administration of a vaccine after October 1, 1988, if the injury or death resulted from side effects that were unavoidable even though the vaccine was properly prepared and was accompanied by proper directions and warnings – §300aa–22( b)(1)
You are right. That is big. Would require lots of popcorn if insurance companies get really gutsy.