Originally Posted by Freebase Dali

If you're a member of the Thieves Guild, you'll have an option to pay off debts at a significantly lower price (or for free) than you would otherwise, but I don't personally know of any way to settle a debt between yourself and a hold via a Thieves Guild proxy.

In any case, try "submitting" when a Falkreath guard attacks. Basically approach one with your weapon drawn, let the guard hit you a couple times, then sheath your weapon. They should then interact with you to prompt you for jail time or payment. Do it several times until it works. If it doesn't work after multiple attempts, trying spending a few days elsewhere and going back and trying it again.

Might not hurt to have a speechcraft buff just in case.