Combine pork ribs, pork shoulder, water, and salt in a Dutch oven over medium heat. Cover and cook, stirring occasionally, for 20 minutes. Uncover and increase heat to medium-high. Continue cooking and stirring constantly until all liquid has evaporated and pork has browned, 15 to 20 minutes.

Combine onion, tomatillos, serrano peppers, and cilantro in a medium saucepan. Add enough water to cover. Bring to a boil and cook until tomatillos are tender and have changed color, 5 to 7 minutes. Transfer vegetable mixture to a blender; add garlic and and blend carefully until sauce is smooth.

Pour sauce into the Dutch oven, season stew with salt and pepper, and simmer for 1 hour. Add purslane and simmer until pork is tender and purslane is soft, about 20 minutes more.