In a saute pan, set over between medium high/medium heat, add the pork belly. (You don't need to add oil.) Cook, stirring occasionally, until brown, and fat has rendered, about 7 minutes. Transfer to a plate. Set aside.
Pour off some of the oil from the pan and leave about 2 tablespoon of the oil. Add the garlic, cook, stirring consistently, until fragrant, soft and light brown but not burned, about 30 seconds. Transfer to a plate.
Add the onion into the pan, cook, stirring occasionally, until soft, about 5 minutes.
Return garlic along with tomatoes to the pan. Reduce heat to medium low. Cover and cook, opening the cover occasionally to stir, until tomatoes have released their juices and become almost like a paste, about 5 minutes. Stir in soy sauce, vinegar, water, black pepper, fish sauce and salt, to taste. Then add the string beans and put cover back on. Bring the heat up to medium high and cook for 1 minute.
Divide among bowls. Serve with steamed rice.