I know that there is no method to find minimum distance when there are negative weight cycles in a graph, there will be no meaning of minimum distance. My question is what will happen if we feed Floyd Warshall Algorithm with graphs having negative weight cycles? Will it run indefinitely or terminate (maybe with wrong answer) in O(n3)?
As you may find on Wikipedia
There are no conditions in Floyd-Warshall algorithms that are based on current weight or maximum weight.
Algorithms just go through all pairs of vertices and calculate distance.
So the answer is No, it will not run indefinitely.
And definitely algorithm will return wrong answer (for vertices in negative cycles you will have negative distances). For example distance from vertex to itself would be negative.
Also this algorithm also can be used for negative cycles detection.