What is the grammatical term (or terms) for this 'object-subject' between two verbs? [duplicate]

Solution 1:

I saw the dog bite the stick.

This is a catenative construction in which "saw" is the catenative verb, and the subordinate clause, "bite the stick", is its catenative complement.

The intervening noun phrase, "the dog", is the syntactic object of "saw" and the understood (semantic) subject of the subordinate clause. It's called a 'raised' object because the verb that it relates to syntactically is higher in the constituent structure than the one it relates to semantically.