This is a fun little rabbit hole. I searched the goddess's name in the Thesaurus Linguae Graecae (the grand database for all Greek texts) and I got a few references. Translations are my own.
The oldest is a comment by Polemon Iliensis (Polemon of Troy/Western Turkey) who probably wrote around the birth of Christ. He wrote travel diaries called 'periegesises' (literally a 'going around' in Greek) which mentions a temple to Adephagia. The original text did not survive antiquity but it is paraphrased by the Sicilian Greek writer Athenaeus in the 3rd century AD in his work Deipnosophistae" Wisemen at Dinner". He tells us,
"Polemon in the first of those (book) to Timaeus, said that among the Sicilians there is a temple of Adaphagia and a statue of Demeter Sitous (the bready-one) near where a statue of Himalis (literally 'abundant' another epithet of Demeter) just as there is one of Hermuchus (Charles Button in his commentary suggests 'unexpected gain') at Delphi, and of Megalaptos (literally 'much bread') and Megalomazos (literally 'much barley' at Skolus and Boetia." Athenaeus Deipnosophistae 416b.
Writing a little earlier the 2nd century AD we have another very similar reference from Greek military writer Aelian that may well have also derived from Polemon, though he does not credit his source. This is given in the context of a list of famous gluttons throughout history,
"It is said that in Sicily there is a temple of Adephagias and a statue of Demeter Sitous.
Aelian, Historical Miscellany 1.27
Returning to your initial question, as you can see from these references, the matter is far from clear cut. Though 'famine' and 'the breaded Demeter' seem opposite theological concepts, the following set of analogies that Athenaeus makes seem to equate the two titles with the same context. 'Unexpected gain' obviously parallels Apollo's oracular nature at Delphi, 'much barley' and 'much bread' follow logically too. This seems to imply an association, even equation, between Demeter and Adephagia. Whether Athenaeus understands them a syncretism (the same goddess) or merely complimentary is difficult to know as the other examples he quoted are not well cited outside this passage.
In either case it seems one plausible answer that Adephagia was either a native deity or local innovation. This is not at all uncommon in the religiously diverse Greek world. It is important to remember that the Greeks were neither native to Sicily nor its only colonists. The island also saw a heavy Carthaginian and Phoenician colonization throughout the classical period and we often see signs of cultural mixing between Greek, Phoenician, and Native Sicilian elements in religious worship (Demeter's cult thrived at Carthage).
A second possibility is that the tale is entirely apocryphal. Hellenistic and Imperial Greek authors were very fond of spinning wild yarns about bizarre peoples, places, and worship practices. Periegesises are especially guilty of this to extent that one might fairly point to it as one of the chief characteristics of genre. The ones we have extent generally celebrate the author writing from the comfort of their study and receiving their insight from the muses rather than the practical travel advocated by geographical writers like Strabo. Indeed, our initial source, at least judging from his name, was a native to Turkey, quite a jump from Sicily. Still, Sicily was a well settled part of the Greek world by the first century AD, so there are reasons to disfavor this explanation.
Whichever explanation you prefer, I hope this was a helpful place to start. I don't think you're going to get any definite answers, but you might be able to make some interesting insights digging into these authors, titles, and literary genres. Attalus has a good translation of the Athenaeus and Penelope has Aelian's text