Place the bacon in a large, deep pan with a lid, and cook over medium-high heat, stirring occasionally, until evenly browned, about 10 minutes. Remove the bacon pieces from the pan, and set aside.
Reduce the heat to medium-low, and stir the sliced onion into the hot bacon fat. Cook and stir the onion until it begins to brown, scraping the bits off the bottom of the pan, about 8 minutes. Add the garlic, and cook and stir 4 more minutes. Return the bacon to the pan, stir in the collard greens, and toss gently until the greens are wilted, about 3 minutes.
Pour in the water to almost cover the collard greens, and stir in the brown sugar, vinegar, crushed red pepper, and salt and pepper. Bring to a boil, cover, reduce heat to low, and simmer the collard greens until very tender, 1 to 2 hours.
About 1/2 hour before serving, stir the cannellini beans into the collard greens, and return to a simmer.