You're absolutely right that it doesn't make any sense from a grammatical point of view. And if you took away the relative clause, der sidder på passagersædet, and just wrote the sentence, I bilen bliver hun erklæret død på stedet, the subject form 'hun' is correct.
Hende, as you know, is the direct and indirect object pronoun form. It is also used as the object of a preposition. But it is used in the subject position if the context is one of emphasis e.g. before a relative clause, hende, der går derhenne, er min nabo, or in a sort of demonstrative construction, hende pigen fra København hedder Lene.
It is also the form used after linking verbs, Det var hende. (It was her.)
...and the form used after end (than) Der er ingen, der er bedre end hende. (Nobody/no one is better than her)
Historically you would probably have to go back a hundred years or more to find 'hun' used consistently as the subject pronoun. You can read more about it in the online dictionary, Ordsprog over det danske sprog. II. hun, — ODS