The threat of it actually being permitted to fail should be fairly strong as a persuader.

Like..well, this is a small scale example, but consider a town's police department. Only the citizens of that town should be funding it. If there's suddenly no funding for it, that can only really mean a few things. If everyone chose to not fund it, let them reap the consequences of no police. That town might burn down, or it could thrive, it depends on the citizens and how well they adjust to having to uphold the law on their own.

If the town burns down (literally or figuratively), it will affect import/export at the least. This causes trouble for outside groups who may have enough incentive to step in and put out the fire. Or, who knows, maybe the town gets quarantined so no one has to deal with them anymore.

It's kind of like legalizing suicide. You couldn't charge anyone in the first place, but there's a fear that everyone might commit suicide if you say it's okay. To me, ancap is like that, where you just bite the bullet and let populations destroy themselves if they choose to, while hoping that instead you end up with a more happy and productive set of remaining populations.