In addition to unbalanced classes, where let's say 2% of data is from a minority class and 98% is from the majority, how do people handle when 2% of data is from the minority and 98% is of an unknown class, but pulled from a known distribution?
Are you suggesting that: 2 percent of samples are positive, drawn from p(x|y=1)
98 percent of samples are drawn from a distribution p(x), but may be either positive or negative?
The setting that you described above is called "positive and unlabeled (PU)" learning. This paper: http://cseweb.ucsd.edu/~elkan/posonly.pdf is one of the seminal articles on the topic (although the equation on the bottom of page 214 contains a statement that may not necessarily hold true). There are quite a lot more recent papers on this topic.