Is it correct to say that this element is both part of the predicate and is a complex subject?

"He was seen running down the street." Is it correct to say that "running down the street" fulfills the predicate while also being part of the subject, a complex subject?

Solution 1:

• He was seen running down the street.

is a complex sentence. It's got two verbs (run and see) used in different forms, and therefore two clauses, one main and one subordinate. In addition, it's had several things done to the main clause -- it's been passivized, and the indefinite agent subject (the 'somebody' that saw him) has been deleted.

Several more things have been done to the subordinate clause -- it's been made into a gerund complement clause, and its subject (him, as in Somebody saw him running down the street) has been raised to be the object of see which gets passivized in the main clause.

The original question asks about the gerund verb phrase running down the street.
For the record, this constituent is not the subject. Of anything.
It is not part of the subject of the main clause, nor of its predicate.
It is, however, part of the object complement clause of see.
Finally, fulfills the predicate is a meaningless phrase and has nothing to do with grammar.