'Rheme' merely refers to that part of the clause which is not 'Theme'. 'Rheme' is a case of 'a presence marking an absence'. Without 'Rheme', 'Theme' extends over the entire clause, meaning that the entire clause becomes the point of departure for the clause as message — a notion which is logically incoherent.
A second point is Fawcett's notion of semiotic categories "existing" or not. Such construals of experience are either functional or not. This is the epistemological position that informs and is informed by Systemic Functional Linguistic Theory.