She is drawing a distinction between what are called a surface subject (grammatical subject) and a deep subject. The deep subject of a sentence in the passive voice becomes the grammatical subject when the passive sentence is rephrased in the active voice.

Generally speaking, both subjects are the agent (the person(s) performing the action).

1) John wrote the books.

John is the agent. John is the grammatical subject. John is also the deep subject.

2) The books were written by John.

John is the agent. John is the deep subject. Book is the grammatical subject (surface subject).

The grammatical subject agrees with the verb in number.

"Grammatical subject", said of a passive construction, is used to mean "subject of the sentence, but not the agent of the action".

'I am asking this, because, while I was studying sentence structure, the author was referring to "subject" of a sentence.'

(1) 'I am asking this'

(2) 'because... the author was referring to "subject" of a sentence'

(3) 'while I was studying sentence structure'

In a sentence in the passive voice, the receiver of the action is both the grammatical/formal subject and the real/notional subject.

In "A new art gallery was opened last Saturday"
"a new art gallery" is the only possible subject of the sentence. It is both the grammatical and the notional subject.

Grammatical and notional subjects don't depend on voice. In "the book was written by John", "John" is not the notional subject for several reasons:
1. "John" is a noun, but it is only part of a prepositional phrase, you can't separate the noun from the preposition andmake it the subject of the sentence.
2. Even if you could separate the prepositional phrase, "John" still wouldn't work as the subject of the verb in the passive voice.
3. "by John" is recognised, as a modifier in the predicate, as the "agent". It appears only in passive sentences.
4. The subject of a sentence is not necessarily the "doer" of the action expressed by the verb; it can also be the "receiver" of the action.

In certain types of sentences, you have both a grammatical and a notional subject, as in cleft and pseudo-cleft sentences:
"It was John who wrote the book."

In the example above, "it" is the grammatical subject because it is only "filling" the usual place of the subject. And "John" is the notional/real subject.

One possible way of analysing this sentence is the following:
"It": grammatical/formal subject (called "anticipatory it").
"John": notional/real subject.
"was who wrote the book": predicate, in which "was" is the head and "who wrote the book" is the predicative/subject complement.

I wish I had more time to add more details, but I hope this helps.

Miriam

Yes, I would definitely call "bureaucrats", "cake" and "leaf" the surface subjects.

As for ergativatity, I'd say it's beyond weird! It gives me a headache!

CJ