Knowing a negative cycle exists is not always enough. Sometimes you want to find which nodes are affected by it. A node is affected if you can reach it from the cycle or if the cycle is on a path to it. Run BFS or DFS from every node that improved in the -th iteration. Any node reachable from these nodes has undefined shortest distance because you can route through the cycle to make the distance arbitrarily negative.
This is necessary when the problem asks if a path exists with finite cost. If the destination is affected by a negative cycle, the answer is that no finite shortest path exists.