I'm coming around to picturing it not so much as breaking or halting the pain signals, but not being super efficient at delivering them. Which for some of us, with chronic pain, delivered day in and day out for years, may have very well developed.
When thinking of pain messages as a body alert system, to let you know that you stepped on a nail so that you can do something about it, it makes sense that the the neural system would want to be very good at telling us that there is a problem, and put everything else on hold so that you can fix that foot!
So my thinking now is that you don't want to ignore the pain, and you don't necessarily always want to interrupt the pain signal because the body is doing its best to let you know there is a problem, and may just keep trying different ways to deliver the message, construct new pathways when one is blocked, etc
But maybe what we CAN do, is recognize that the panic state that we may go into after receiving the pain messages, can be increasing the problem, as the brain reacts and subconsciously sends orders all around the body, increasing adrenaline levels, tightening muscles to get them ready to run from the monster that attacked our foot, etc and there's your pain cycle or loop
So ultimately, I'm thinking acceptance-
a neutral response to pain that neither ignores it, so that it tries harder, or an overreaction that increases it
Definitely a paradox!