Did the white stringy stuff come out of the side of the fish or underneath the fish? If it came out from under the fish (between the belly and tail) then it was probably poo. If it came out of the fish's side (between the belly and tail) then it could be something else, perhaps excess mucous.
It depends on what the internal problem is but it could be an internal bacterial infection or intestinal worms. Bacterial infections can be a problem but sometimes respond to treatment if you catch them early enough. Worms will live in fish for years and not cause any major problems unless their numbers build up. Then they slowly suck the life out of the fish.
If the fish is still eating and swimming around normally then it is most likely worms, but if the fish has stopped eating then it is probably an internal bacterial problem and there isn't much you can do.
Bacterial infections can be picked up from bad food or the fish just gets run down and becomes infected from the bugs living in the tank water.
Other fish can be infected with the diseases and there is a possibility they already are. However, a lot of problems only affect the weaker fish leaving the healthy ones untouched. Keeping the tank nice and clean through regular water changes and gravels cleans, and keeping the filter clean will help the fish stay healthy. Dirty tanks, filters and gravel are the biggest cause of fish health problems.