In the bowl of a slow cooker, combine the tomato sauce, chili powder, brown sugar, coriander, and cumin. Stir to combine. Add the pork and salt and pepper the meat. Use tongs to turn the pork over and salt and pepper the other side. Continue to turn until it is coated evenly in the sauce. Add the garlic and onions and stir again.
Place the lid on the slow cooker and cook until tender and beginning to fall apart, 8 to 10 hours on low or 4 to 6 hours on high.
Transfer the pork to a serving plate or bowl. Let cool slightly, then use two forks to shred the meat, removing any excess fat.
Skim any excess fat off the remaining sauce in the slow cooker. Stir in the lime juice and season with salt and pepper. Add the shredded pork back into the sauce and mix until coated.
To assemble the tacos, heat a corn tortilla according to package directions. Place a spoonful of meat down the center of the tortilla and top with desired garnishes such as cabbage, cilantro, and cojita cheese.