When encountering someone stuck in an Apology Loop, I do not uselessly ask, or worse, demand that they “stop apologizing.”
Rather, I have found it much more useful to affect a theatrical tone and formally “absolve” them. “Like a Renaissance pope, I absolve you, my child.” Usually the combination of having the absurdity of the situation highlit, combined with a touch of physiological release if I can get a laugh, is enough to soothe their nerves a bit and get them to break the loop. And who knows maybe they feel absolved I dunno I have an authoritative bearing
This counts as a spell
The last person who got stuck in an overapologizing loop in my house was a long-time friend. That is why I felt that I could get away with.
Throwing myself on the floor at her feet, and rolling back and forth on my back, wailing and sobbing, "Oh I'm Sorry I'm sor SORRY I'm sorry I'm breathing I'mm TOO MUCH I'm Sorry I'm . . "
She was looking down at me, first in bafflement, then very thoughtful. I wrapped it up and got back to my feet. Dusted myself off (dog fur). "Honey," I told her quietly, "I don't need you to do that to me. It doesn't make my life any better when you apologize too much. It puts a burden on me to make YOU feel better about whatever you're upset about."
Pretty, um, aggressive behavior mod on my part. However, I do know her very, very well. And vice versa; it's not like I was any less of a maniac when I was 15. And she does have the emotional maturity to self-reflect. It ended up being a good moment for the two of us, and hopefully gave her a chuckle later on when she told her husband.
Not an widely-useful strategy at all, though.