How long is the longest I can slow cook pork shoulder?

According to Modernist Cooking Made Easy (emphasis added):

For medium rare cooked pork shoulder, the meat should be held at 135°F or 57.2°C, while medium cooked meat is done at 145°F or 62.8°C. If a traditional well done shoulder is desired, it should be cooked at 155°F or 68.3°C. No matter what temperature range is used, the pork shoulder should be cooked for 1 to 2 days. For a crisp or well done outer part, sous vide pork shoulder may be finished by searing, grilling or torching.

Note that to safely maintain and control temperatures this low for the sustained period of time, you must have a proper sous-vide setup, with a means of maintaining the temperature of the water bath.

Even at 135 F, over several hours, the method is safe because the killing of pathogens is a function of both time and temperature.

Similarly, the conversion of gelatin to collagen which gives slow cooked pork its unctuous texture is also a function of both time and temperature. While in more traditional cooking methods (oven or barbecue), reaching internal temperatures of about 180 F is necessary to get collagen conversion in a reasonable period of time, it can be done in the truly extended time periods sous-vide cooking makes possible.

For more traditional cooking methods, about 225 F is about as low as you want to go

See also:

• Why would a pressure cooker shorten a braise time? which looks at this question from the other end, making the conversion more rapid, and describes collagen to gelatin conversion in more detail.

The lowest simmer is about 180-185F. That's about as low as you'd want to go. Theoretically, you could go lower (and you certainly could go lower for sous-vide), but significantly lower in the oven or on the stove leaves little margin of error for safety. You'd want to cook your shoulder to at least 160F because that's the temperature at which collagen begins to break down. Depending upon the size of your roast, that could easily be as long as 24 hours.

EDIT: in response to OP's edit: 10 Lbs? You could go 24 hours. Since the temperature if your simmering liquid or oven is only 180-185, the roast isn't going to get higher than that, so if you want to go as long as 24 hours, you'd be fine. Again, with the strict temperature control of sous-vide, you could go longer, but with less precise control of temperature 24 hours is plenty, personally I wouldn't go longer than that.