>>11963546My understanding is that as a grandparent or great grandparent passes, the ring is then held for the upcoming generation.
You would have several cyclical rings in circulation for a family. I have my Great Grandmother's gold and blue topaz ring, but it was for a place holder until I could get something more specific.
Alternatively, as parents get older and build more wealth or lose it all, they tend to get different rings anyway. Stands to reason they could pass on the family ring and replace it with a simpler band.