The Many-seeded Sanwort was probably described in 1846 (the author is sometimes given as C. Gay).
The species was apparently endemic to a small area in the IV Coquimbo Region of northern Chile and appears to be lost or even extinct.
 Clodomiro Marticorena; Francisco A Squeo; Gina Arancio; Mélica Muñoz: Catálogo de la Flora Vascular de la IV Región de Coquimbo. Libro Rojo de la Flora Nativa y de los Sitios Prioritarios para su Conservación: Región de Coquimbo (F. A. Squeo, G. Arancio y J. R. Gutiérrez, Eds.) Ediciones Universidad de La Serena, La Serena, Chile 7: 105-142. 2001
Gay’s Knapweed was described in 1849 based on material that had been collected somewhere in the hills of the Coquimbo Province, Chile.
The species is furtermore known to have also occurred in the Atacama region of the Huasco Province. 
I was not able so far to find any furter information about this enigmatic species.
 Diego Penneckamp; Rodrigo Chaura; Gloria Rojas; Tod Stuessy: Taxonomic notes on Plectocephalus (Centaurea s.l., Centaureinae, Asteraceae) from Chile, including new combinations and synonyms. Phytotaxa 437(4): 227-236. 2020
The distribution of this species was limited to the coastal cliffs of the island of Alejandro Selkirk, then still called Más Afuera, in the Juan Fernández archipelago of Chile.
It was a kind of miniature version of a tree rarely more than 50 cm high, with a 10 to 20 cm high, about 1 cm thick trunk that was more or less covered by dead leaves. The leaves themselves were very narrow, almost ribbon-like, and were described as strongly succulent.
The photo below is from 1920 and shows a plant that was sown in 1919 and bloomed just a year later.
Unfortunately, the specimen pictured died without producing any fertile seeds, otherwise the species might still exist today, even if only in cultivation.
The last representatives of this species were found in 1991, two already badly battered specimens were all that was left over from the insatiable hunger of the introduced goats that were found all over the island. All later search expeditions were completely unsuccessful – the species is now extinct.
… macabre but true:
These goats, for their part, are widely regarded as a special breed (Juan Fernández goats) and are kept in zoos that specialize in keeping rare or even endangered breeds of domestic animals.
 C. Skottsberg: Notas sobre la vegetación de las Islas de Juan Fernández. Anales J. Bot. Madrid 11: 515-544. 1953  Marcia Ricci: Conservation status and ex situ cultivation efforts of endemic flora of the Juan Fernández Archipelago. Biodivers Conserv 15:3111–3130. 2006  Francis Hallé; Philippe Danton; Christophe Perrier: Architectures de plantes de l’Íle Robinson Crusoe, archipel Juan Fernández, Chili. Adansonia 29(2): 333-350. 2007