Okay, this thread inspired Adam and I to do some writing. It's not in the PDF yet, but here's the idea:
When you drop to 0 HP, you're dying. You can't go negative. Immediately make the dying move.
When you're dying, you catch a glimpse of what lies beyond the black gates of death, roll (just roll, +nothing). On a 10+ you're stable. On a 7-9 death offers you a choice, give Death one of your moves and live to see another day or pass beyond the black gates into whatever fate awaits you. If you give a move to Death, mark it off your character sheet, you can't regain that move unless you undertake a perilous quest to wrench it from Death's grasp. On a 6-, you're dead.
Someone who's stable at 0 can be healed normally.
Natural healing takes place whenever you Make Camp, or when the GM thinks you've had enough rest to heal up. You heal your Con modifier plus your level in HP.