Hello this is a picture of a popular wine. The ring around the bottle is twisted closed. Before you open the bottle, the cork is in the top of the bottle and another wire wrapped enclosure is on top of the cork and hooks underneath the ring you see attached to the bottle. By unwinding the ring that is attached to the bottle you loosen it and the top wire cap lifts off leaving just the cork which is then removed.
Note- The top part of the wire enclosure never fully winds around the bottom ring that holds it in place. As you see in the images it has a ‘foot’ or a hook, that just hooks under the wire ring that can remain on the bottle or be fully unwound and removed if desired.
This enclosure is done because the wine is fizzy. If there was no wire holding the cork in place it would (and has) pops off. Is it permitted to unwind this type of wire closure on Shabbos? I have attached multiple images of the wire enclosures.
It is permitted to open and close then on Shabbos. Although there is controversy regarding twist ties, if they may be opened and closed on Shabbos. Most authorities hold that it is permitted, and although some people are stringent with this, the halacha is that essentially it is permitted. Additionally, this case is even better than that, because here you are not fashioning anything, because the metal is already wound together. You are only tightening and loosening the already wound tie. Therefore everyone would agree in this case that it is permitted. Additionally, the bottom ring is similar to a lock that is evident that it is made to open and close constantly, and therefore permitted.
Regarding twist ties- Emes L’yackov ftnt. 360, Divrei Yatziv O:CH 152, Ohr L’tzion 2 chap. 29-2, Shevet Halevi 8-55, 10-61, Chut Shani Shabbos 2 pg. 228, Igros Moshe and Beer Moshe quoted in The Shabbos Home 14 ftnt. 12, Orchos Shabbos 10 ftnt. 51, Am Mikadshei Sheviei 2 chap. 5 ftnt 37, Megillas Sefer 21-6, Nitei Gavriel ( Erev Pesach On Shabbos) 17-18. SS”K 16 ftnt. 174,
Regarding your question- numerous poskim.