For sure. Seems hard to say, I'll bow to anyone's superior knowledge since I'm speculating right now, but I reckon a ring system may sometimes be a sort of natural optimizer which finds a stable configuration where they're far enough away to avoid the atmosphere and sparse enough that the effects between particles are negligible. The mechanism I propose here is that the most unstable parts of the system might deorbit first, leaving behind something stable.

Again, wanton speculation from someone on the internet who's qualifications are that they thinks this is an interesting question to consider, don't take it anymore seriously than that.