There is nothing to worry infact this suggest that there digestion system is working properly as that brown string which you are talking about is there stool
Fish of any species can have fecal strands that stay attached to their rectum. Common fish species are goldfish and plecostomus that have this problem.. It can be disturbing to see this. Most of the time it is nothing to worry about, but there are a few ailments that can cause this problem. The key is recognising problems so you know what to do. Check out www.wetwebmedia They are very helpful if you need questions answered to most of your fish problems.
See how long it has a brown string. If it's a long time for it to fall off it's constipated. If it's not it's pooping.
No its just natural its a fishes way of emptying its bowels.
Your goldfish's plumbing is working good. It's just going to the bathroom. It will fall off and sink to the bottom. That's why it's important to keep their bowl clean.
Don't worry. I have three goldfish. They have it once in a while. I think it is just poop.
My goldfish string hs gone red is this normal