As noted in the other question, stars can form rings around them. We call them circumstellar disc. But can stars can have "Saturn-like" rings that had a formation mechanism similar to Saturn (which are thought to be pieces of comets, asteroids or shattered moons that broke up before they reached the planet, torn apart by Saturn's powerful gravity)? The answer is "speculative". However, I found two cases:
LSPM J0207+3331, a white dwarf is thought to have rings. The reason is unknown but scientists speculates that:
[...] some white dwarfs — between one and four percent — show infrared emission indicating they’re surrounded by dusty disks or rings. Scientists think the dust may arise from distant asteroids and comets kicked closer to the star by gravitational interactions with displaced planets. As these small bodies approach the white dwarf, the star’s strong gravity tears them apart in a process called tidal disruption.
The debris forms a ring of dust that will slowly spiral down onto the surface of the star.