Say I'm trying to predict negative profits of jobs completed. (to catch them before they go bad) There are seldom in the dataset and may even be considered outliers to the rest of the data. Is this possible? Is it just the case that a good fit will get the job done?
Your question is too general, theoretically what you ask can be done. Imagine the following scenario: You build a linear model say $y=a_0 + a_1*x_1 + ... + a_n*x_n$. It could be that one of our regressors i.e one $x_i$ is binary that is $x_i=0,1$ then for the outliers this $x_i$ could be one in your data and thus every "outlier" would be "predictable" by your linear model. All in all the answer is that yes it is possible, but I highly doubt this is your case if you are using real-world data, usually outliers would not be detectable from your regressors given the coefficients of your model.