In Sentence #1, “What she is going through is called being in labor,” the gerund phrase “being in labor” is not a subject complement. It’s functioning as an adverbial modifier of the verb “called.” That gerund phrase will function as a subject complement if the verb “called” is dropped so the sentence will read as follows: “What she is going through is being in labor.” Here, “being in labor” is now a subject complement linked to the subject “what she is going through” (a relative noun clause) by the linking verb “is.”
In Sentence #2, “I saw him wearing a red shirt,” the word “wearing” is neither a gerund nor a participle. It’s the progressive form of the verb “wear,” indicating a continuing past action, and the phrase “wearing a red shirt” functions as an adjective phrase modifying the pronoun “him.”
In Sentence #3, using the pronoun “him” will make the sentence read as follows: “I dislike him wearing a red shirt.” Here, the word “wearing” is the progressive form of the verb “wear,” indicating a continuing past action as in Sentence #2 above; the phrase “wearing a red shirt” is an adjective phrase modifying the pronoun “him.” On the other hand, when the pronoun “his” is used, the sentence will read as follows: “I dislike his wearing a red shirt.” This time, the phrase “his wearing a red shirt” is a gerund phrase that functions as an adverbial modifier of the verb “dislike.”
