Will cooking chicken longer in soup make it less tough and stringy?
There's several major reasons why meat and poultry can be tough:


Collagen: muscles exist to impart a force between bones, when they contract there must be a connection between that muscle and the bone or the muscle would not be able to do work. Collagen is a strong protein that is distributed throughout a muscle and connects to a tendon, allowing the muscle to distribute its' force to the skeletal structure of the animal. The more load a muscle takes, the more collagen is needed to distribute the force, and the tougher the meat is. 
The animal was stressed before slaughter: if the animal was stressed before slaughter it will have lactic acid buildup resulting in tougher meat
Poor treatment after slaughter: Once an animal dies chemical changes happen that toughen the meat, and the correct treatment is needed to allow the meat to relax again. If that isn't done right you'll get tough meat
Freezing and thawing: freezing makes meat and poultry tougher


Collagen breaks down in the presence of heat and moisture, so a long stewing at low temperature could make your chicken tender. The collagen helps make your broth thicker and taster too! That would take a maximum of 2-3 hours on a low simmer. If it isn't tender by then it isn't tough because of collagen and there isn't much you can do. If you've got a chicken that was stressed, not processed correctly, and then frozen there's a limit to how tender you'll be able to get it.  You can try cooking it a couple more hours, but if it isn't tender by then it never will be.