Halliday & Matthiessen (2014: 394):
… while the Thing … is the entity that is functioning as participant in the transitivity structure of the clause … It is the Head that determines the value of the entity in the mood system, and therefore as a potential Subject.
To demonstrate:
Here it is clearly the word picture that serves as Thing, since it was the picture that was eaten by the llama, not Dorian Grey.
For Matthiessen (1995: 656-7), on the other hand, it is Dorian Grey that serves as Thing in such nominal groups:
