My terminology isn't great, but what I'm talking about in practice is usually what happens as the next step after someone gets talked down from using existential types all over the place.

I'm personally a big fan of existential types, but they usually don't need to be explicit. One place that shows up on Hackage that's worth studying is Edward Kmett's `folds` library. The type, Data.Fold.L.L is a codata type

    data L = forall r . L (r -> b) (r -> a -> r) r	 

It uses existential typing for efficiency, but doesn't need to. Instead, it just helps to show the encapsulation going on here---you literally cannot examine `r` in any way besides applying some of the bundled functions (methods, destructors).

The existential type highlights that L is acting as codata, but it's usually not recommended in practice as existential types are a little hard to manage. You could write L more simply and eliminate the `r` data

    data L = L b (a -> L)

by just pre-applying the existentially typed data to each of its destructors and rebundling new L types where necessary.

In any case, the point is that it's easy to build a variety of L variants, but hard to extend new operations on Ls.