Is it possible to convert a graph with one negative capacity to a graph with only positive capacities?
If you indeed have an edge $e$ with a negative capacity, and, I assume, it is a directed edge having no corresponding opposite edge, then you can reverse $e$, make its capacity positive, and, then, solve a regular max-flow problem with all capacities being non-negative. (Look at the concept of the residual network to understand what a negative capacity means.) Make sure you are not confusing edge capacities with costs.