In a paper that I am currently writing, we have an individually-authored appendix, although the author of the appendix is also a co-author on the paper.

In this situation, the appendix is a relatively long and technical proof of a fact that is used peripherally in the paper. The proof is not sufficiently important to the main thrust of the paper to be incorporated into the body of the paper, and the major results of the paper do not rely on it. However it provides an explanation for some of the phenomena we describe (and prove) in the paper. Although this self-contained fact is not proved in the literature, it is probably not enough to make a separate paper without the context and motivation provided by the rest of the paper. As it is solely my coauthor's work it makes sense to include it separately with only his name attached.

I imagine that the same applies to an appendix with a separate author not among the main authors - a piece of work that is self-contained, of sufficient scale and scope that it warrants separate authorship, and yet whose significance is greatly enhanced by the motivation, context and results of the main paper.