I quite like the term “rare” languages. It’s much better than ‘exotic’ and it has the connotation of something valuable without necessarily harping on the ‘death’ aspect of language death.
The term ‘rare languages’ was used in a number of media reports on the State Library of New South Wales’ digitisation of early settler Aboriginal vocabularies. The items include the Blackburn Eora vocabulary and Mary Cain’s Coonabarabran district vocab lists from 1920. There are transcriptions as well as images of the originals.
The rest of the site is also worth exploring!