The languages will go not because they're forced to go but because they're not sufficiently useful.
With them will go some distinctions made for cultural reasons. Mostly they'll be carried forward. Irish culture is still Irish using English. Carry over a few dozen terms specific to a culture and it'll go. (In other words, the correlation of culture/language is just that. It's like the correlation between skin color/teeth shape and speaking Zulu or Tuvan. It's strong but accidental.)
There's lots of work done in showing why language shift occurs. There's been lots of attempt to halt or reverse it. Few have been very successful in the relatively short term (meaning a generation). Most have just failed. Some successes confuse documentation or recording a token or two of each word with the language.
We have a grip on what language is. We have a decent idea about phonological representation and its origins. We have a fairly good idea about a lot of phonetic processes and language change. We know a fair amount about some syntaxes.
Yet the first impulse is to write down paradigms and record word tokens because grant-providers think those are the essence of language, stuck in the 1300s with word lists and text grammars. Even those resurrecting Cornish as a 2nd language (or ben Yehudah) don't get it right: all the things that make up a language, all the diversity of styles and registers, webs of connotations and denotations, usus and praxis, die long before the last speaker dies. They resurrect not the original language, but a kind of linguistic homunculus--which promptly becomes a person in its own right, a la Pinocchio.