What is the fatty tissue in beef/pork after it has been braised/stwed? Perhaps this question has been asked before, but I am unable to find it. The closest I got was someone asking about chicken skin after frying.

When a piece of meat with large nuggets or fat attached is braised or boiled, the fat can be seen on the surface of the braising liquid. 
When it has been cooked for long enough, no more oil/fat is being given off by the piece of meat, but the (often) whitish/yellow tissue remains. 
It has a really soft and melty texture but doesn't really seem fatty. 

I personally really like this. But what is it actually?
is it still fat? Is it healthy?
That is a type of protein and connective tissue. 
Mainly you have collagen and elastin in a cut of meat.

Collagen turns into gelatin through heating and melts away. The elastin will get softened. I believe what you’re seeing is the elastin.