Tropical fish (and probably ALL fish) can get something called dropsy, which is where the intestinal tract clogs up and the fish can't eliminate. Effectively, it gets stopped up with fecal matter, swells up, gets toxic, and dies. It's a horrible way to go. Good reason to feed your fish some fiber, to keep 'em regular. (I give my bettas minced corn germ or beans, and the pond fish fresh corn.)
But since your friend's fish is eating and eliminating, the problem sounds more like a tumor to me. Like a non-malignant tumor that keeps growing, but hasn't invaded any other organs.
Can you get a picture?