Halliday & Matthiessen (2014: 140):
The Subject, when it first appears, may be any nominal group. If it is a personal pronoun, like he, it is simply repeated each time. If it is anything else, like the duke, then after the first occurrence it is replaced by the personal pronoun corresponding to it. … Nominal groups functioning as Subject include embedded, down-ranked clauses serving as Head… . In ‘circumstantial’ relational clauses, the Subject may be a prepositional phrase or an adverbial group.