Can a subject ever be part of a prepositional phrase? Why or why not.

Yes, I think you can get into debate on what such a phrase is, and whether a preposition is being used as a preposition.

In a sentence, every verb must have a subject. If the verb expresses action-likesneeze, jump, bark, or study-the subject is who or what does the verb. Take a look at this example: During his biology lab, Tommy danced on the table. Danced is an action verb. Tommy is who did the dancing. Look at the next example: The speeding hotrod crashed into a telephone pole. Crashed is the action verb. The hotrod is what did the crashing. Not all verbs are action verbs. Some verbs are linking: am, is, are, was, were, seem, and become, among others. Linking verbs connect the subject to something that is said about the subject. Take a look at this example: Ron's bathroom is a disaster. Bathroom is the subject. Is connects the subject to something that is said about it, that the bathroom is a disaster. Here is another example: The bathroom tiles are fuzzy with mold. The word tiles is the subject. Are connects tiles to something said about them, that they are fuzzy with mold. Generally, but not always, the subject of a linking verb will come before the linking verb.