If you mean their strategy is to sue the hospital she was in previously in a different state, I don't think NJ law would give them any claim.
I also think people are confused about NJ law. NJ law has a different definition of legal death from other states - it is not making a medical judgment. 'Actual' death, brain death, and legal death are all different things I guess the best comparison would be the opposite - life. 'Actual' i.e. biological life begins at conception, legal life in some states begins then and in others at viability, and legal life with full rights begins at birth. You can have a fetus without a brain that is 'alive' but only in the most basic sense. You can have 2 separate embryonic lives that fuse into conjoined twins, which legally will be two lives if that twin is developed, and one life it is merely parasitic. Biologically, there are still two lives involved. Then you have all sorts of religious beliefs about when death and life are recognized. Doctors have never argued that brain death and death are the same thing - effectively in terms of future prospects, they are, but it's obviously not the same biological state. N.J. doesn't tell people how to define brain death - it tells them that brain death cannot result in legal death if that conflicts with religious beliefs. Brain death gives permission for legal death, but not a guarantee. Same with a person missing for a long time - eventually you can have them declared legally dead, in accordance with that state's rules - obviously, that may or may not be true - it's just what the state is choosing to recognize, and it can vary.