I don't have any idea how to do this, and my research keeps coming up short, so I am hoping someone can supply me with some resource/idea of how to do this. What I would like to do is have a pathfinder that finds a path that leads away from a target position on a 2d tile-map. Anything is helpful, but there just isn't much that I've found regarding a pathfinder that can pathfind away from something.
since you do not specify what programming language nor target environment, what I can suggest is to take a look at this demo project. There is a visualizer of the algorithms used to find a path from the start to the finish point including obstacle done in JavaScript. The project is called Pathfinder JS.
PS: I do not have any association with the project