Prep the vegetables: finely chop the onion and celery; peel and dice the potatoes into 0.5-inch cubes. Remove the skin from the chicken thighs if still attached.
Heat the vegetable oil in a large heavy pot over medium heat. Add the onion and celery and cook, stirring occasionally, until softened and translucent, 6–8 minutes.
Stir in the canned crushed tomatoes, chicken stock, apple cider vinegar, Worcestershire sauce, light brown sugar, kosher salt, and black pepper. Bring to a gentle simmer.
Nestle the chicken thighs into the pot. Maintain a gentle simmer and cook uncovered until the meat pulls easily from the bone, 30–35 minutes, skimming any foam as needed.
Transfer the chicken to a board and cool briefly. Shred the meat and discard the bones; return the shredded chicken to the pot.
Add the pulled pork, potatoes, frozen baby lima beans, and frozen corn kernels. Simmer, stirring every few minutes to prevent sticking, until the potatoes are tender and the stew is very thick and spoon-standing, 30–40 minutes. Add a splash of water if the pot becomes too dry before the potatoes are done.
Stir in the hot sauce. Taste and adjust seasoning to balance savory, tangy, and sweet notes.
Let the stew rest off the heat for 10 minutes to settle and thicken further, then serve hot.