Idea: Ask what breaks Dijkstra but not Bellman-Ford.
Dijkstra locks in a vertex once picked and never revisits it, so a later negative edge cannot correct the distance. It therefore cannot cope with, or flag, negative cycles.
Bellman-Ford instead relaxes every edge repeatedly. After $|V| - 1$ rounds all true shortest distances are fixed if no negative cycle exists. Run one more round:
\[ \text{if } dist[v] > dist[u] + w(u,v) \text{ still improves, a negative cycle is present} \]
because in a graph with no negative cycle nothing can improve after $|V| - 1$ rounds. That extra check is the feature Dijkstra lacks.
\[\boxed{\text{Negative weight cycles}}\]