I don't mean to scare or worry you, but this in my view is not normal. The isolation fish may have some health problem, but these are usually very difficult to ID as external symptoms may be absent or misleading. The sheltering in an upper corner can be from aggression, water issues, or internal protozoan.
Which brings me to aggression. Tetras are shoaling fish that live in large groups, and they must have adequate sized groups of their own species in an aquarium. Emperor Tetras (species is Nematobrycon palmeri) can get a bit feisty, so this is a species I would never suggest be fewer than 7-8, and preferably 9-10. They can develop quite an hierarchy, I've had to get rid of them for just this issue. Getting a few more if you want to keep this species would be strongly advised. However, don't expect that to "cure" the isolated fish, it will likely not recover regardless of what is the issue.
Which species are "fire tetra?" If by chance it is Aphyocharax rathbuni, which I have seen under this common name, you may have more trouble, as all species in this genus are feisty to say the least. It too needs a much larger group, but its fin nipping may become an issue regardless so think this through. I've no idea what other fish you have or intend, nor the tank size.