But, no need to cry and reach for the scissors. It is possible to open a closed ring - at a picot.
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What usually works for me is to spread the stitches as much as possible at a picot, preferable the one nearest to the end of the ring. Then I reach down in there with a crochet hook, and insert the shaft under the core thread. The core needs to be pulled in the same direction as when opening a ring normally while working. Pinch the double stitches at the end where the core is sliding, to help prevent them from turning and getting so tight that the core cannot slide.
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Triumph!
BTW, the photos show just a peek of part of a larger project that I am in the process of designing - to be revealed at a later date :-)