Question: You end up bleeding to death and you have a choice of being treated by vaccinated or unvaccinated - presumably you don't care which.
Answer to your question - I've told my wife to sue any hospital that causes a deterioration in my condition due to any action they have failed to take to optimise my care. Whether that's Hep B, Covid or leaving a lump of plastic inside me doesn't matter.
What about a fully vaxxed doctor giving it to you?
In any case, I think any litigation would seriously struggle to prove a particular individual was the vector.