Vaccine liability claims in the United States are handled by the federal government [0].

I can guarantee with absolute certainty that we won’t see this same situation with COVID vaccines, as Pfizer, Moderna, and J&J don’t have any liability for their vaccines, as they were created during a public health emergency [1][2]

The reasoning is nobody would make vaccines if they had unlimited liability.

[0] https://en.m.wikipedia.org/wiki/National_Vaccine_Injury_Comp... [1] https://en.m.wikipedia.org/wiki/Public_Readiness_and_Emergen... [2] https://www.law.cornell.edu/uscode/text/42/247d-6d