Basically, for an unsupervised task, it's nonsense data that does not fall under any meaningful class in the training dataset. It can be anything. In the paper, they modify each MNIST image so that it isn't a digit anymore but looks like one. The network doesn't generate negative images, you do, and feed it as "bad data" right after you give it "good data" to create contrast between them for the model to learn.

For a supervised task, "bad data" can also be nonsense (just as in unsupervised task) or can be mislabeled data such as feeding an image of "5" but embedding "4" as the label inside the image. That's obviously wrong, and is considered bad data.