The way I see it, "cup" is the primary subject but is understood to mean "quantity of ice cream that is in the cup". If "of strawberry ice cream" is sufficiently well indicated by the context, it would be possible to simply say "The cup melted completely" with the same meaning.
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AnonymousCan the object of a preposition ever be the simple subject of the sentence?The answer to that question is dependent on the analytical method you are using. A method that emphasizes syntax will give the answer "no" and will designate "cup" as the simple subject. A method that emphasizes semantics may answer "yes" and may designate "ice cream" as the