A periodic structure also can place subordinate phrases and clauses between the subject and predicate. Sophisticated writers use periodic structure to lengthen sentences without losing control of them. Periodic sentences also can be particularly useful as you make transitions between your body paragraphs. In the introductory phrase or clause, you may refer to the matter of the previous paragraph, then refer to your new matter in the main part of the sentence. But it's not.
Pronouns can function as subjects in sentences or as objects.
Me and him went fishing. If you have trouble figuring out the case of your pronouns, you may do better to recast the sentence than to spend time and energy trying to solve the riddle of the case. Problems with case are a good sign that you need to establish your agent more strongly. Remember that when pronouns follow prepositions, they most likely are objects of the preposition. Personal pronouns replace a noun antecedent, and their relationship to that noun should be clear.