Pork Loin in Soup

Pork tenderloin (hence the "tender" in tenderloin) is lovely and tender all by itself when quickly cooked (oven or stove), so as Chef Ono indicates, it isn't a tough cut that requires braising or other lengthy, slow, cooking to become tender. Left over could easily be added (shredded or cubed) to a soup or similar preparation.

Because the tenderloin is a naturally tender cut (whether pork or beef or any other animal), it also tends to be an expensive cut that can stand on its own very nicely (or with a nice sauce over it). Other, tougher and less expensive cuts can serve very well in a soup or stew or any other long, slow, cooking preparation.

Having said all that, if pork tenderloin is what you have and what you want to use, I would treat it the same as a boneless chicken breast both for size of cuts (I'd probably cube it) and length of cooking. It will cook remarkably quickly, and like a boneless chicken breast it won't have alot of flavor to add to the soup -- rather, prolonged cooking could suck the flavor out of the meat leaving you only with the texture to chew on. A half inch cube would probably be cooked in 5 to 10 minutes -- and you can always pull one out and cut it if you want to double check.

I have used leftover cooked pork tenderloin, shredded, in soups and stews. Added it to the other ingredients about 15 minutes before I expected the dish to be done and it was just fine.

The problem with that idea is there's very little connective tissue in loin meat. No connective tissue = no collagen = no gelatin. It's contrary to the whole concept of braising / stewing. Plus there's relatively little fat and fat = flavor.

Your grocer will gladly sell you smaller cuts from the same part of the pig. Look for blade steaks or ask the guy behind the counter for assistance. Smaller cuts will come at a price however. The economical approach is to think of all the other ways to use a pork butt and make good use of your freezer (and your grinder if you have one).