Combine the tomato sauce, chili powder, brown sugar, coriander and cumin in the base of your slow cooker. Stir to combine and distribute the spices evenly.
Sprinkle the pork with salt and pepper and place it in the slow cooker. Using tongs, turn the pork to coat it evenly in the sauce. Add in the garlic and onions, stir again. Place the lid on the slow cooker and cook until the pork is tender and beginning to fall apart, on low 8 to 10 hours or on high 4 to 6 hours.
Transfer the pork to a serving bowl. Allow to cool slightly, and then shred using 2 forks, removing any excess fat.
Skim any excess fat off of the sauce remaining in the slow cooker. Stir in the lime juice and season with salt and pepper. Add the shredded pork back into the slow cooker and mix it with the sauce that was created during the cooking. You can store the pork in its sauce for 3 to 4 days.