Isn't the language almost extinct and the community almost wiped out? I remember reading a while back that there are only a few hundred speakers and as more canadians move into the area, the inuit community and language were being endangered. Is there a systematic campaign to preserve the language and/or community? At the very least to set down the vocabulary/grammer/pronounciation/etc?
Every tribe is working very hard on language preservation and some are getting much better results than others. Some have been lost, but the folks in Alaska are putting a lot of effort into it. I asked a question on HN for a grant that was directed about using ML to aid in language preservation. I didn't get any responses. We were trying to expand the tools available.
If you approach the problem instead from the language preservation perspective and ask what is necessary to make it succeed, there are essentially two tasks: documentation (recording current speakers' knowledge of the language) and community maintenance (allowing people to keep using the language and teaching it to the next generation).
Documentation basically boils down to making a lot of recordings. Since text is usually nicer to work with, transcriptions are very useful, and in theory ML would be able to help with that, but to train a speech-to-text model, you first need transcribed training data, leading to a chicken-and-egg problem. Making the data easily available and easy to contribute to is more likely to be impactful.
For maintaining a community, ML can be useful by providing all the services that ML offers for speakers of more popular languages: text-to-speech, speech-to-text, predictive smartphone keyboards, machine translation, ... but all of those depend on the language being well-documented already. Otherwise, non-ML solutions are likely to be the only options (so formant-based speech synthesis e.g. with espeak-ng, dumb keyboards, rule-based translators, ...)
To give a specific example, I know of a community of Kabyle speakers who want to be able to use OpenStreetMap with voice navigation in Kabyle, so they've been making a lot of recordings (using https://tatoeba.org as a platform for the documentation part) and also have someone working on a speech-synthesis model (using Mozilla's DeepSpeech, I think). AFAIK, the project is coordinated by Muhend Beqasem, whom you might want to contact if you're interested in what they're doing: https://tatoeba.org/eng/user/profile/belkacem77