Suppose you brine a chicken in a heavy solution e.g. 10% saline. Suppose you now boil this chicken in water which does not contain salt or contains a little salt e.g. 5g. How much of the salt, if any, will come out of the chicken and go into the soup. Will it try to equalise via osmoses and keep putting salt out until an equal concentration is present in chicken and soup or not? If it does, i take it a large amount of salt will ditribute into the soup liquid leaving the chicken less salty?
I'm not exactly sure why you're trying to brine then boil; you should be able to simply boil your chicken in salty stock and get plenty of salt into it. It won't take nearly as long as brining, because things happen faster in boiling water.
Assuming you boil for any significant length of time, much of the salt will indeed come out into the cooking liquid, and you'll end up with your soup approximately as salty as the chicken. (If the chicken is in large pieces, this of course only applies to the part the brining and cooking liquids can actually reach.)
It seems like you would season the water/stock with salt from the meat. The amount is unreliable, and would be based on cooking time, salinity of the meat, size of cut, mineral content of the water, etc.
I am not sure about meat, but a few answers regarding potatoes on a quick google search state that boiling denatures protiens and ruptures cell membranes. That means that the salt water in the meat is simply diffusing out into the normal water. At some point an equilibrium would occur. I can't remember enough chemistry to tell you whether this would happen before or after the meat finished cooking. It would follow that for cuts of beef and chicken with similar salt content by weight, you would notice a difference in salinity of the cooking liquid due to the structure/density of the meat, given all other factors were equal.
Cooking meat tightens up the protiens, which is what causes it to squeeze out the juices. The point of brining is to add extra (flavorful) juices to the meat, so it won't dry out as much at cooking time. Since you have to cook meat for a long time in water to dry it out, the problem in this question can be avoided by boiling unbrined meat, and seasoning the water as you cook. Even with a brined, salted, or pickled meat, you will still want to taste as you cook, and season to taste.
Not enought reputation for a third link, but copy and paste is a thing www.cookingforengineers.com/article/70/Brining