Actually plenty of businesses fail at adapting. Most of the time you can blame managerial error (or liquidity issues like right now) for the demise of an enterprise. But yeah, you can tell a survival of the fittest story and evolutionary economics, following in the steps of Schumpeter. is an important research area (especially in a discipline with an equilibrium fetish).
Of course unions do are ideologically, just like me, social democratic and thus for the moderation of capitalist excesses, for the smoothing of the business cycle, for employment stability and so on.
Yet I don't think that this stands in contrast to economic adaptation but actually enhances it. Scandinavian countries feature e.g. extremely liberal hire&fire labour markets with a broad welfare state that eases the costs of frequent employment changes.
On the other hand you are of course correct that workers value employment stability and unions fight for things like the auto bailout (which did make some economic sense as there are network effects / negative externalities , i.e. an automobile company is a bit like a bank, when it goes down many other companies go down ... but of course one still has to ask whether companies like Chrysler who produced crap for years will magically start to improve right now), i.e. for a lack of adaption.