Changes

Pure speculation: I think that the individual rings belonging to each Horsemen, symbolically represents their implement or implements they traditionally bear or carry in lore. For instance, Famine's ring symbolizes the set of scales used in lore, War's ring symbolizes his red sword used in lore. And as for Death and Pestilence's representations, Death isn't foretold to be bearing a weapon but in many depictions, he bears a scythe; and Pestilence is often incorporated with Death. That why they disassemble when they lose physical connection with their ring except for Death. What does anyone else think on the matter?