One very concrete example of this stabilization is when you no longer have to close your eyes (or keep them closed) to maintain contact with a particular field. You can include the external environment in your experience now too. To me this feels like the beginnings of a marriage between the inner and outer worlds. What once seemed so flat and irrelevant out there as compared to my rich inner experience, now is being infused with more light, connection, depth, meaning. The contacts are being repaired. This is the advantage of increasing stabilization. A rippling, emergent intimacy.
I still close my eyes a lot (when not meditating), but now I try to do it only as much as necessary.