As the Wikipaedia article suggests, the objective case is typical for such nominals. In Latin and Greek, for example, the accusative case is used—although neither language normally has this expletive there expressed as a special word, the below is semantically identical to using English there is/are:
Dicit viros adesse [acc. mascl. plural]
"He says men to be present = He says that there are men (there/present)".
It is the same in Ancient Greek.
In English, the objective case is used in similar constructions (though without your sense of there):
He is there --> I want him to be there.
He is a teacher --> I want him to be a teacher.
It is clear that *
I want he to be there is unacceptable. Both these examples and your example are historically the same construction in English.
It is the same in Dutch, with the sense of there you are looking for (er):
Hij was er --> Ik zag hem er zijn [note that the construction is a little bit contrived with this particular sense of the verb and the pronoun combined, but it's possible].
"He was there" --> "I saw him there be = I saw him be there".