I guess auto-immune disease is an example of where it also goes the wrong way for somebody. Probably most of us know somebody with IBD, lupus, or any of the others. It's very common for the body to reject something benign, or ourselves.
Type 1 diabetes is a good example of this, where the body detects its own insulin producing cells as threats and eliminates them. Lots of the research in type 1 treatments isn't just about producing insulin, but figuring out how to prevent the body from destroying it again without all of the risks of immunosupressant drugs.